In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and D...In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.展开更多
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic par...An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic partial differential equations (PDEs). The use of the BHSDA to solve PDEs is facilitated by the method of lines which involves making an approximation to the space derivatives, and hence reducing the problem to that of solving a time-dependent system of first order initial value ordinary differential equations. The stability properties of the method is examined and some numerical results presented.展开更多
In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obta...In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obtain some new criteria for all solutions of certain neutral hyperbolic partial functions differential equations to be oscillatory.展开更多
In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo...In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.展开更多
In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local trunc...In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.展开更多
In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular ...In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).展开更多
In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j...In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.展开更多
This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations,...This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.展开更多
Some new oscillation criteria are established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [...Some new oscillation criteria are established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [11].We remove some assumptions that are required for the related results in the previous papers,thus our results generalize and improve many known conclusions.展开更多
Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we es...In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.展开更多
In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori er...In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.展开更多
Under a non-Lipschitz condition being considered as a generalized case of Lipschitz condition, the existence and uniqueness of mild solutions to neutral stochas- tic functional differential equations driven by fractio...Under a non-Lipschitz condition being considered as a generalized case of Lipschitz condition, the existence and uniqueness of mild solutions to neutral stochas- tic functional differential equations driven by fractional Brownian motion with Hurst parameter 1/2 〈 H 〈 1 are investigated. Some known results are generalized and im- proved.展开更多
Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form pa...Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form partial derivative u/partial derivative t - partial derivative/partial derivative x(a(x,y,t) partial derivative u/partial derivative x) - partial derivative/partial derivative y(b(x,y,t) partial derivative u partial derivative y) = f Two A.D.I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L-2 energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called 'equivalence between L-2 norm and H-1 semi-norm'. In this paper, we try to improve these conclusions by H-1 energy estimating method. The principal results are that both of the two A.D.I. schemes are absolutely stable and converge to the exact solution with error estimations O(Delta t(2) + h(2)) in discrete H-1 norm. This implies essential improvement of existing conclusions.展开更多
This paper discusses the oscillation of solutions for nonlinear neutral partial differential equation in the form of Sufficient conditions are obtained for oscillation of solutions,of this equation, which extend and ...This paper discusses the oscillation of solutions for nonlinear neutral partial differential equation in the form of Sufficient conditions are obtained for oscillation of solutions,of this equation, which extend and improve some known results. Where n is bounded domain in R' with piecewise smooth boundary and △is the Laplacian in Euclidean n -space R'.展开更多
In this paper,we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations(BSDEs).By the nonlinear Feynman-Kac formula,we reformulate the BSDE into a pair of referen...In this paper,we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations(BSDEs).By the nonlinear Feynman-Kac formula,we reformulate the BSDE into a pair of reference ordinary differential equations(ODEs),which can be directly discretized by many standard ODE solvers,yielding the corresponding numerical schemes for BSDEs.In particular,by applying strong stability preserving(SSP)time discretizations to the reference ODEs,we can propose new SSP multistep schemes for BSDEs.Theoretical analyses are rigorously performed to prove the consistency,stability and convergency of the proposed SSP multistep schemes.Numerical experiments are further carried out to verify our theoretical results and the capacity of the proposed SSP multistep schemes for solving complex associated problems.展开更多
文摘In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
文摘In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
基金the Natural Science Foundation of Hunan Province(10471086)the Science Research Foundation of Administration of Education of Hunan Province(07C164)
文摘In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.
文摘The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
文摘An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic partial differential equations (PDEs). The use of the BHSDA to solve PDEs is facilitated by the method of lines which involves making an approximation to the space derivatives, and hence reducing the problem to that of solving a time-dependent system of first order initial value ordinary differential equations. The stability properties of the method is examined and some numerical results presented.
文摘In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obtain some new criteria for all solutions of certain neutral hyperbolic partial functions differential equations to be oscillatory.
基金Supported by the National Natural Science Foundation of China(10471086).
文摘In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.
文摘In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.
基金This work is supported by the National Fujian Province Nature Science Research Funds
文摘In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).
基金Supported by the National Natural Science Foundation of China
文摘In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.
基金Supported by Natural Science Foundation of Hebei Province（102160） and Natural Science of Education office in Hebei Province （2004123）,
文摘This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.
基金supported by the National Natural Science Foundation of China (10771118)the Fund of Subject for Doctor of Ministry of Education (20103705110003)the Natural Science Foundations of Shandong Province (ZR2009AM011 and ZR2009AL015)
文摘Some new oscillation criteria are established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [11].We remove some assumptions that are required for the related results in the previous papers,thus our results generalize and improve many known conclusions.
文摘Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
基金the Natural Science Foundation of Hunan Province under Grant 05JJ40008.
文摘In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.
基金National Nature Science Foundation under Grants 60474027 and 10771211the National Basic Research Program under the Grant 2005CB321701
文摘In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.
文摘Under a non-Lipschitz condition being considered as a generalized case of Lipschitz condition, the existence and uniqueness of mild solutions to neutral stochas- tic functional differential equations driven by fractional Brownian motion with Hurst parameter 1/2 〈 H 〈 1 are investigated. Some known results are generalized and im- proved.
文摘Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form partial derivative u/partial derivative t - partial derivative/partial derivative x(a(x,y,t) partial derivative u/partial derivative x) - partial derivative/partial derivative y(b(x,y,t) partial derivative u partial derivative y) = f Two A.D.I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L-2 energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called 'equivalence between L-2 norm and H-1 semi-norm'. In this paper, we try to improve these conclusions by H-1 energy estimating method. The principal results are that both of the two A.D.I. schemes are absolutely stable and converge to the exact solution with error estimations O(Delta t(2) + h(2)) in discrete H-1 norm. This implies essential improvement of existing conclusions.
文摘This paper discusses the oscillation of solutions for nonlinear neutral partial differential equation in the form of Sufficient conditions are obtained for oscillation of solutions,of this equation, which extend and improve some known results. Where n is bounded domain in R' with piecewise smooth boundary and △is the Laplacian in Euclidean n -space R'.
基金supported by the National Natural Science Foundations of China(Grant Nos.12071261,11831010)the National Key R&D Program(Grant No.2018YFA0703900).
文摘In this paper,we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations(BSDEs).By the nonlinear Feynman-Kac formula,we reformulate the BSDE into a pair of reference ordinary differential equations(ODEs),which can be directly discretized by many standard ODE solvers,yielding the corresponding numerical schemes for BSDEs.In particular,by applying strong stability preserving(SSP)time discretizations to the reference ODEs,we can propose new SSP multistep schemes for BSDEs.Theoretical analyses are rigorously performed to prove the consistency,stability and convergency of the proposed SSP multistep schemes.Numerical experiments are further carried out to verify our theoretical results and the capacity of the proposed SSP multistep schemes for solving complex associated problems.
