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The Numerical Solution of BVPs for a Class of Functional Differential Equations

Author: HuangLiWen
Tutor: ZhangChengJian
School: Huazhong University of Science and Technology
Course: Computational Mathematics
Keywords: Boundary value problem Delay differential equations Runge-Kutta method Block boundary value method
CLC: O175.8
Type: Master's thesis
Year: 2011
Downloads: 22
Quote: 0
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Abstract


Functional boundary value problems into the application of optimal control theory and circuit theory . Differential Problems relative functional , in theory, has greater difficulties to solve this kind of problem , so as to construct a numerical algorithm and the corresponding theoretical analysis it is particularly important . Configuration method and differential method has been used to solve Functional Differential Equations with Boundary Value , but its theoretical analysis is not very unified . This article aims to construct a class of higher order differential method and its unified convergence analysis . We know that the theory and numerical solution of ordinary differential equations has close ties with the theory and numerical solutions of the corresponding initial value problem . Keller had a differential format application compatibility and stability to the existence and uniqueness of solutions of first order ordinary differential boundary value problem , if and only if this format is applied to the corresponding initial value problem is compatible and stable , that is, and so price convergence . Functional differential equations boundary value problem with the initial value problem is similar intrinsic link ? Linear paper will give an affirmative answer . In this paper, the Runge-Kutta method and the block boundary value method is applied to solve a class of linear functional differential equations boundary value problem and give a convergence analysis . Functional Differential Equations with Boundary Value for the existence and uniqueness of solutions , we prove that the general format of differential convergence of order p if and only if this difference scheme applied to the corresponding functional Differential Problems convergence order p . By the Runge-Kutta method and the block boundary value method for solving the initial value problem of convergence , we get the Runge-Kutta method and the block boundary value method is applied to the convergence of Functional Differential Equations with Boundary Value . Finally , the numerical results verify our theoretical analysis .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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