A Collocation Method for the Numerical Solution of Non-linear Parabolic Partial Differential Equations

Lagrange interpolation formulae are used to obtain a new algorithmfor the approximate polynomial solution of linear and non-linearparabolic equations. The algorithm is described for problemsin one space dimension, although it is applicable to problemsdefined in two or more dimensions. It is also shown how thealgorithm may be adapted to solve a moving boundary (Stefan)problem.     

非局部初边值条件下的抛物型偏微分方程

本文讨论在非局部初边值条件下的抛物型偏微分方程,在更为宽松的边界假设条件下讨论所构造的迭代序列的收敛速度问题.并且对非局部初值条件为离散形式的情况做了相应的讨论.     

The Numerical Solution of Parabolic Partial Differential Equations Using the Method of Lanczos

Several types of parabolic equations are solved, subject tovarious boundary conditions. A polynomial solution is sought,which is the exact solution of a perturbed version of the originaldifferential equation. The method is developed for the heatequation and then extended to a wide range of problems.     

A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations

In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.     

Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

In this paper, we present and analyze a single interval Legendre-Gauss spectral collocation method for solving the second order nonlinear delay differential equations with variable delays. We also propose a novel algorithm for the single interval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy of the proposed methods.     

On Chebyshev Solution of Parabolic Partial Differential Equations

Now at Mathemarics Department, Assiut University Egypt A method is presented to transform parabolic equations to asystem of ordinary differential equations for the solution atthe Chebyshev points. The system may be solved analyticallyor by numerical methods and the Chebyshev coefficients are computed.We have the exact solution of a perturbed problem.     

A Note on the Numerical Solution of Quasi-linear Parabolic Partial Differential Equations with Error Estimates

A method is considered for the numerical solution of quasi-linearpartial differential equations. The partial differential equationis reduced to a set of ordinary differential equations usinga Chebyshev series expansion. The exact solution of this setof ordinary differential equations is shown to be the solutionof a perturbed form of the original equation. This enables errorestimates to be found for linear and mildly non-linear problems.     

Spectral Method for Nonlinear Stochastic Partial Differential Equations of Elliptic Type

This paper is concerned with the numerical approximations of semi-linear stochastic partial differential equations of elliptic type in multi-dimensions. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method. Numerical results demonstrate the good performance of the spectral method.     

The Numerical Solution of the Fourth Boundary Value Problem for Parabolic Partial Differential Equations

A direct method for the numerical solution of the implicit finitedifference equations derived from a parabolic differential equationwith periodic spatial boundary conditions is presented in algorithmicfrom. Consideration is given to the stability of the roundingerrors involved in the solution process and numerical resultsare derived which compare favourably with those obtained fromthe analytical solution and a matrix spectral resolution methodwhich is closely allied to the method of lines.     

非线性抛物型偏泛函微分方程的渐近行为

本文研究一类非线性抛物型偏泛函微分方程的渐近行为。采用上下解方法,建立了其解的有界性和稳定性,通过半群理论、非负矩阵性质和不等式技巧,得到估计这类方程平衡态渐近稳定域的方法。     

Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations

In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differentialequations with smooth coefficients and some initial conditions,by the way,we obtain the quasi-surecontinuity of the solution.     

A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients

We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements related to lower bounds of small denominators appearing in the course of solution of the problem.     

中立抛物型偏微分方程解的强迫振动

本文讨论一类多滞量中立抛物型偏微分方程解的振动性质 ,获得了其一切解振动的充分条件 ;指出了与普通抛物型偏微分方程质的差异 .     

脉冲中向量中立型抛物偏微分方程的H-振动性

研究一类脉冲向量中立型抛物偏微分方程的振动性,借助Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲中立型微分不等式不存在最终正解的问题,建立了该类方程在Dirichlet边值条件下所有解H-振动的若干充分判据,这里H是R~M中的单位向量.     

Existence of Solutions for Impulsive Parabolic Partial Differential Equations

We discuss the propagation of heat along a homogeneous rod of length A under the influence of a nonlinear heat source and impulsive effects at fixed times. This problem is described by an initial-boundary value problem for a nonlinear parabolic partial differential equation subjected to impulsive effects at fixed times. Using Green's function, we convert the problem into a nonlinear integral equation. Sufficient conditions are provided that enable the application of fixed point theorems to prove existence and uniqueness of solutions.     

Linear Second-Order Partial Differential Equations of the Parabolic Type

The article is a review of the theory of linear partial differential equations of the parabolic type, where the classical facts of this theory are described in detail. Bibliography: 128 titles.     

Generalized Solutions of Linear Parabolic Stochastic Partial Differential Equations

Existence and uniqueness theorems for parabolic stochastic partial differential equations with space—time white noise are proved. The method is a combination of the characterization theorem for Hida distributions with the Feynman—Kac and Girsanov formulae. Accepted 3 December 1996     

Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations

In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions, by the way, we obtain the quasi-sure continuity of the solution.     

Neumann Boundary Problems for Parabolic Partial Differential Equations with Divergence Terms

Potential Analysis - In this paper, we give a probabilistic interpretation for solutions to the Neumann boundary problems for a class of semi-linear parabolic partial differential equations (PDEs...