We introduce the radiation transport equations, the radiation fluid mechanics equations and the fluid mechanics equations with quantum effects. We obtain the unique global weak solution for the radiation transport flu...We introduce the radiation transport equations, the radiation fluid mechanics equations and the fluid mechanics equations with quantum effects. We obtain the unique global weak solution for the radiation transport fluid mechanics equations under certain initial and boundary values. In addition, we also obtain the periodic region problem of the compressible N-S equation with quantum effect has weak solutions under some conditions.展开更多
Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical method...Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical methods when applied to stochastic Hamiltonian partial differential equations (PDEs), such as long-time behavior, geometric structure preserving, and physical properties preserving. Stochastic Maxwell equations driven by either additive noise or multiplicative noise are a system of stochastic Hamiltonian PDEs intrinsically, which play an important role in fields such as stochastic electromagnetism and statistical radiophysics. Thereby, the construction and the analysis of various numerical methods for stochastic Maxwell equations which inherit the stochastic multi-symplecticity, the evolution laws of energy and divergence of the original system are an important and promising subject. The first stochastic multi-symplectic method is designed and analyzed to stochastic Maxwell equations by Hong et al.(A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise. J. Comput. Phys. 268:255-268, 2014). Subsequently, there have been developed various stochastic multi-symplectic methods to solve stochastic Maxwell equations. In this paper, we make a review on these stochastic multi-symplectic methods for solving stochastic Maxwell equations driven by a stochastic process. Meanwhile, the theoretical results of well-posedness and conservation laws of the stochastic Maxwell equations are included.展开更多
In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by W...In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.展开更多
In this note we derive MHD boundary layer equations according to viscosity and resistivity coefficients. Especially, when these viscosity and resistivity coefficients are of different orders, it leads to degenerate MH...In this note we derive MHD boundary layer equations according to viscosity and resistivity coefficients. Especially, when these viscosity and resistivity coefficients are of different orders, it leads to degenerate MHD boundary layer equations. We prove these degenerate boundary layers are stable around a steady solution.展开更多
Lyapunov direct method is employed to investigate the asymptotic behaviour and the boundedness of solutions to a certain third-order differential equation with delay and some new results are obtained. Our results impr...Lyapunov direct method is employed to investigate the asymptotic behaviour and the boundedness of solutions to a certain third-order differential equation with delay and some new results are obtained. Our results improve and complement some earlier results. Two examples are given to illustrate the importance of the topic and the main results obtained.展开更多
Hot air producing is one of the most important engineering applications in recent years.It is a technique used in various thermodynamic systems,such as home heating systems,food dryers.One of the main problems impedin...Hot air producing is one of the most important engineering applications in recent years.It is a technique used in various thermodynamic systems,such as home heating systems,food dryers.One of the main problems impeding the spread of hot air producing technology is the lack of homogeneity of the heat flow coming from hot air generators as well as an inadequate flow rate.The most of the existing hot air generators require to be supported by systems that can increase the low volumetric flow and the air temperature of these generators,through increasing the speed of the flow of air emitted or lifting the drawer Heat,which contributes to raising the overall cost.However,to improve the thermal and dynamic quality of the hot air flow produced by the generator,a numerical investigation of the free convection flow inside two different configurations is presented in this thesis.The primary objective of this work is to predict the behavior of the flow inside tow configurations,the first one consists of a vertical cylinder with heated walls,and the second configuration is an open-ended vertical cylinder with a hot disc placed at the entrance(configuration A,configuration B).This work characterizes through the examination of this flow,the variables that control an air emission with high flow rate and a high and homogeneous temperature to represent the appropriate criteria that should be respected to obtain a hot air generator overcoming the previously mentioned constraints.Furthermore;the results of this work show the influence the boundary conditions and Rayleigh number on the resulting flow.展开更多
We report some novel dynamical phenomena of dissipative solitons supported by introducing an asymmetric wedge-shaped potential (just as a sharp 'razor')into the complex Ginzburg-Landau equation with the cubicq...We report some novel dynamical phenomena of dissipative solitons supported by introducing an asymmetric wedge-shaped potential (just as a sharp 'razor')into the complex Ginzburg-Landau equation with the cubicquintic nonlinearity.The potentials corresponding to a local refractive index modulation with breaking symmetry can be realized in an active optical medium with respective expanding antiwaveguiding structures.Using the razor potential acting on a central dissipative soliton,possible outcomes of asymmetric and single-side splitting of dissipative solitons are achieved with setting different strengths and steepness of the potentials.The results can potentially be used to design a multi-route splitter for light beams.展开更多
Most unsteady channel flows in nature and practical engineering appear as gradually varied ones,and in the free surface,the deformation conforms to the long wave hypothesis.One-dimensional total flow models were usual...Most unsteady channel flows in nature and practical engineering appear as gradually varied ones,and in the free surface,the deformation conforms to the long wave hypothesis.One-dimensional total flow models were usually used to for the numerical simulation of long-term and long-distance reaches to describe the water movements,however,the models lack a clear relationship between the three-dimensional flow field and the total flow field.Moreover,few studies of the variations of the roughness coefficient against the time in unsteady flows were conducted.The following results are obtained through the theoretical analysis and the numerical simulations in this paper.(1) One-dimensional total flow control equations of the unsteady gradually varied flow in open channels are obtained directly from the mathematical model of the viscous fluid motion,and can both reflect the influence of the turbulence and provide an explicit expression of the energy slope term.These equations establish a direct connection between the descriptions of the three-dimensional flow fields and the one-dimensional total flows.(2) Synchronous prototype observation data and planar two-dimensional numerical simulation results are used to extract the one-dimensional total flow information and discuss the total flow characteristics.(3)The orders of magnitude for terms in the total flow motion equation are compared,and the variation of the roughness coefficient against the time is analyzed.展开更多
Inasmuch as the hydrostatic structure of the interior of neutron stars uniquely depends on the equation of state(EOS), the inverse constraints on EOS from astrophysical observations have been an important method for r...Inasmuch as the hydrostatic structure of the interior of neutron stars uniquely depends on the equation of state(EOS), the inverse constraints on EOS from astrophysical observations have been an important method for revealing the properties of high density matter. Currently, most EOS for neutron star matter are given in tabular form,but these numerical tables can have quite different resolution. To guarantee both the accuracy and efficiency in computing the Tolman-Oppenheimer-Volkoff equations, a concise standard for generating EOS tables with suitable resolution is investigated. It is shown that EOS tables with 50 points logarithmic-uniformly distributed in the supra-nuclear density segment [ρ0, 10ρ0], where ρ0 is the nuclear saturation density, correspond to the interpolation induced errors of ~0.02% for the gravitational mass M and ~0.2% for the tidal deformability ∧.展开更多
In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the loca...In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.展开更多
This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jac...This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jacobi polynomials on the reference square, we construct the C1-conforming basis functions using the bilinear mapping from the reference square onto each quadrilateral element which fall into three categories-interior modes, edge modes, and vertex modes. In contrast to the triangular element, compulsively compensatory requirements on the global C1-continuity should be imposed for edge and vertex mode basis functions such that their normal derivatives on each common edge are reduced from rational functions to polynomials, which depend on only parameters of the common edge. It is amazing that the C1-conforming basis functions on each quadrilateral element contain polynomials in primitive variables, the completeness is then guaranteed and further confirmed by the numerical results on the Petrov-Galerkin spectral method for the non-homogeneous boundary value problem of fourth-order equations on an arbitrary quadrilateral. Finally, a C1-conforming quadrilateral spectral element method is proposed for the biharmonic eigenvalue problem, and numerical experiments demonstrate the effectiveness and efficiency of our spectral element method.展开更多
Preface This Special Issue in'Acta Mathematicae Applicatae Sinica(English Series)'gathers peer reviewed papers dedicated to Professor Philippe G.Ciarlet on the occasion of his eightieth birthday.Written by fri...Preface This Special Issue in'Acta Mathematicae Applicatae Sinica(English Series)'gathers peer reviewed papers dedicated to Professor Philippe G.Ciarlet on the occasion of his eightieth birthday.Written by friends and colleagues from France and Hong Kong/China,they stand as a testimony of their admiration for an exceptional human being and mathematician.展开更多
The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter ...The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur'e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.展开更多
The aim of this paper is to introduce and solve the p-radical functional equation f(p√x^p+y^p)=f(x)+f(y),p∈N2.We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate s...The aim of this paper is to introduce and solve the p-radical functional equation f(p√x^p+y^p)=f(x)+f(y),p∈N2.We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.展开更多
In this article, regularity of the global attractor for atmospheric circulation equations with humidity effect is considered. It is proved that atmospheric circulation equations with humidity effect possess a global a...In this article, regularity of the global attractor for atmospheric circulation equations with humidity effect is considered. It is proved that atmospheric circulation equations with humidity effect possess a global attractor in H~k(?, R~4) for any k≥0, which attracts any bounded set of H~k(?, R~4) in the H~k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor.展开更多
In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error est...In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.展开更多
One of the solution techniques used for ordinary differential equations, partial and integral equations is the Elzaki Transform. This paper is an extension of Mamadu and Njoseh [1] numerical procedure (Elzaki transfor...One of the solution techniques used for ordinary differential equations, partial and integral equations is the Elzaki Transform. This paper is an extension of Mamadu and Njoseh [1] numerical procedure (Elzaki transform method (ETM)) for computing delay differential equations (DDEs). Here, a reconstructed Elzaki transform method (RETM) is proposed for the solution of DDEs where Mamadu-Njoseh polynomials are applied as basis functions in the approximation of the analytic solution. Using this strategy, a numerical illustration as in Ref.[1] is provided to the RETM as a basis for comparison to guarantee accuracy and consistency of the method. All numerical computations were performed with MAPLE 18 software.展开更多
This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampere equation detD^2u{x)= b(x)f(u(x)),u> 0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N...This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampere equation detD^2u{x)= b(x)f(u(x)),u> 0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C^∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.展开更多
文摘We introduce the radiation transport equations, the radiation fluid mechanics equations and the fluid mechanics equations with quantum effects. We obtain the unique global weak solution for the radiation transport fluid mechanics equations under certain initial and boundary values. In addition, we also obtain the periodic region problem of the compressible N-S equation with quantum effect has weak solutions under some conditions.
基金The research of L.Zhang was supported by the NNSFC(NOs.11601514,11771444,and 11801556)the research of C.Chen and J.Hong were supported by the NNSFC(NOs.91630312,11711530071,and 11871068)the research of L.Ji was supported by the NNSFC(NOs.11601032,and 11471310).
文摘Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical methods when applied to stochastic Hamiltonian partial differential equations (PDEs), such as long-time behavior, geometric structure preserving, and physical properties preserving. Stochastic Maxwell equations driven by either additive noise or multiplicative noise are a system of stochastic Hamiltonian PDEs intrinsically, which play an important role in fields such as stochastic electromagnetism and statistical radiophysics. Thereby, the construction and the analysis of various numerical methods for stochastic Maxwell equations which inherit the stochastic multi-symplecticity, the evolution laws of energy and divergence of the original system are an important and promising subject. The first stochastic multi-symplectic method is designed and analyzed to stochastic Maxwell equations by Hong et al.(A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise. J. Comput. Phys. 268:255-268, 2014). Subsequently, there have been developed various stochastic multi-symplectic methods to solve stochastic Maxwell equations. In this paper, we make a review on these stochastic multi-symplectic methods for solving stochastic Maxwell equations driven by a stochastic process. Meanwhile, the theoretical results of well-posedness and conservation laws of the stochastic Maxwell equations are included.
基金NSF(Grant No.DMS-1600028)NSF-FRG(Grant No.DMS-1463753)+1 种基金NSF(Grant No.DMS-1362940)a Sloan Research fellowship.
文摘In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.
基金NSFC (Grant No. 11671067)NSFC under grant 11671067,"the Fundamental Research Funds for the Central Universities", and China Scholarship Council.
文摘In this note we derive MHD boundary layer equations according to viscosity and resistivity coefficients. Especially, when these viscosity and resistivity coefficients are of different orders, it leads to degenerate MHD boundary layer equations. We prove these degenerate boundary layers are stable around a steady solution.
文摘Lyapunov direct method is employed to investigate the asymptotic behaviour and the boundedness of solutions to a certain third-order differential equation with delay and some new results are obtained. Our results improve and complement some earlier results. Two examples are given to illustrate the importance of the topic and the main results obtained.
文摘Hot air producing is one of the most important engineering applications in recent years.It is a technique used in various thermodynamic systems,such as home heating systems,food dryers.One of the main problems impeding the spread of hot air producing technology is the lack of homogeneity of the heat flow coming from hot air generators as well as an inadequate flow rate.The most of the existing hot air generators require to be supported by systems that can increase the low volumetric flow and the air temperature of these generators,through increasing the speed of the flow of air emitted or lifting the drawer Heat,which contributes to raising the overall cost.However,to improve the thermal and dynamic quality of the hot air flow produced by the generator,a numerical investigation of the free convection flow inside two different configurations is presented in this thesis.The primary objective of this work is to predict the behavior of the flow inside tow configurations,the first one consists of a vertical cylinder with heated walls,and the second configuration is an open-ended vertical cylinder with a hot disc placed at the entrance(configuration A,configuration B).This work characterizes through the examination of this flow,the variables that control an air emission with high flow rate and a high and homogeneous temperature to represent the appropriate criteria that should be respected to obtain a hot air generator overcoming the previously mentioned constraints.Furthermore;the results of this work show the influence the boundary conditions and Rayleigh number on the resulting flow.
基金the National Natural Science Foundation of China under Grant No 61665007the Natural Science Foundation of Jiangxi Province under Grant No 20161BAB202039.
文摘We report some novel dynamical phenomena of dissipative solitons supported by introducing an asymmetric wedge-shaped potential (just as a sharp 'razor')into the complex Ginzburg-Landau equation with the cubicquintic nonlinearity.The potentials corresponding to a local refractive index modulation with breaking symmetry can be realized in an active optical medium with respective expanding antiwaveguiding structures.Using the razor potential acting on a central dissipative soliton,possible outcomes of asymmetric and single-side splitting of dissipative solitons are achieved with setting different strengths and steepness of the potentials.The results can potentially be used to design a multi-route splitter for light beams.
基金the National Key Projects of China (Grant No.2018YFC0407603).
文摘Most unsteady channel flows in nature and practical engineering appear as gradually varied ones,and in the free surface,the deformation conforms to the long wave hypothesis.One-dimensional total flow models were usually used to for the numerical simulation of long-term and long-distance reaches to describe the water movements,however,the models lack a clear relationship between the three-dimensional flow field and the total flow field.Moreover,few studies of the variations of the roughness coefficient against the time in unsteady flows were conducted.The following results are obtained through the theoretical analysis and the numerical simulations in this paper.(1) One-dimensional total flow control equations of the unsteady gradually varied flow in open channels are obtained directly from the mathematical model of the viscous fluid motion,and can both reflect the influence of the turbulence and provide an explicit expression of the energy slope term.These equations establish a direct connection between the descriptions of the three-dimensional flow fields and the one-dimensional total flows.(2) Synchronous prototype observation data and planar two-dimensional numerical simulation results are used to extract the one-dimensional total flow information and discuss the total flow characteristics.(3)The orders of magnitude for terms in the total flow motion equation are compared,and the variation of the roughness coefficient against the time is analyzed.
基金National Natural Science Foundation of China (11722546 and 11275073)Talent Program of South China University of Technology (K5180470).
文摘Inasmuch as the hydrostatic structure of the interior of neutron stars uniquely depends on the equation of state(EOS), the inverse constraints on EOS from astrophysical observations have been an important method for revealing the properties of high density matter. Currently, most EOS for neutron star matter are given in tabular form,but these numerical tables can have quite different resolution. To guarantee both the accuracy and efficiency in computing the Tolman-Oppenheimer-Volkoff equations, a concise standard for generating EOS tables with suitable resolution is investigated. It is shown that EOS tables with 50 points logarithmic-uniformly distributed in the supra-nuclear density segment [ρ0, 10ρ0], where ρ0 is the nuclear saturation density, correspond to the interpolation induced errors of ~0.02% for the gravitational mass M and ~0.2% for the tidal deformability ∧.
基金supported by National Natural Science Foundation of China (Grant No. 11571128).
文摘In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.
文摘This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jacobi polynomials on the reference square, we construct the C1-conforming basis functions using the bilinear mapping from the reference square onto each quadrilateral element which fall into three categories-interior modes, edge modes, and vertex modes. In contrast to the triangular element, compulsively compensatory requirements on the global C1-continuity should be imposed for edge and vertex mode basis functions such that their normal derivatives on each common edge are reduced from rational functions to polynomials, which depend on only parameters of the common edge. It is amazing that the C1-conforming basis functions on each quadrilateral element contain polynomials in primitive variables, the completeness is then guaranteed and further confirmed by the numerical results on the Petrov-Galerkin spectral method for the non-homogeneous boundary value problem of fourth-order equations on an arbitrary quadrilateral. Finally, a C1-conforming quadrilateral spectral element method is proposed for the biharmonic eigenvalue problem, and numerical experiments demonstrate the effectiveness and efficiency of our spectral element method.
文摘Preface This Special Issue in'Acta Mathematicae Applicatae Sinica(English Series)'gathers peer reviewed papers dedicated to Professor Philippe G.Ciarlet on the occasion of his eightieth birthday.Written by friends and colleagues from France and Hong Kong/China,they stand as a testimony of their admiration for an exceptional human being and mathematician.
文摘The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur'e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.
文摘The aim of this paper is to introduce and solve the p-radical functional equation f(p√x^p+y^p)=f(x)+f(y),p∈N2.We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.
基金Supported by the National Natural Science Foundation of China (No.11701399).
文摘In this article, regularity of the global attractor for atmospheric circulation equations with humidity effect is considered. It is proved that atmospheric circulation equations with humidity effect possess a global attractor in H~k(?, R~4) for any k≥0, which attracts any bounded set of H~k(?, R~4) in the H~k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor.
基金the National Natural Science Foundation of China(Nos.11461068,11362021,and 11401511)the Doctoral Foundation of Xinjiang Uygur Autonomous Region of China(No.BS110101).
文摘In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.
文摘One of the solution techniques used for ordinary differential equations, partial and integral equations is the Elzaki Transform. This paper is an extension of Mamadu and Njoseh [1] numerical procedure (Elzaki transform method (ETM)) for computing delay differential equations (DDEs). Here, a reconstructed Elzaki transform method (RETM) is proposed for the solution of DDEs where Mamadu-Njoseh polynomials are applied as basis functions in the approximation of the analytic solution. Using this strategy, a numerical illustration as in Ref.[1] is provided to the RETM as a basis for comparison to guarantee accuracy and consistency of the method. All numerical computations were performed with MAPLE 18 software.
文摘This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampere equation detD^2u{x)= b(x)f(u(x)),u> 0, x∈Ω, where Ω is a strictly convex and bounded smooth domain in R^N with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b∈C^∞(Ω) is positive in Ω, but may be appropriate singular on the boundary.