一类混合型积分微分方程的数值解法
A Numerical Solution of Mixed Integral Differential Equations
摘要: 多项式逼近在数学分析和数值逼近理论中具有重要的地位，它已广泛应用于工程计算和实际生活中。而且关于积分微分方程数值解法的研究一直是存在于各领域的重要课题。本文主要基于Legendre多项式重新构建再生核，通过Gram-Schmidt给出方程的近似解。同时，给出三个Volterra-Fredholm积分微分方程的数值算例，与传统的再生核方法进行数值比较，进一步验证了我们方法是有效的，且具有很高的精度。所有数值计算都是通过数学软件Mathematica8.0给出。
Abstract: Polynomial approximation in the mathematical analysis and numerical approximation theory has an important position; it has been widely used in engineering calculation and the actual life. And the study of the numerical method for solving the integral differential equation is one of the im-portant subjects exists in every field. This paper mainly based on Legendre polynomial rebuilding the reproducing kernel, through the “Gram-Schmidt”, the approximate solution of the equation is given. At the same time, it gives three numerical examples of Volterra-Fredholm integral differen-tial equation. Compared with the traditional methods of reproducing kernel, we further verified that our method was effective and had high precision. All numerical calculations are given by the Mathematica 8.0 software.
文章引用：刘杨, 王玉兰. 一类混合型积分微分方程的数值解法[J]. 应用数学进展, 2018, 7(7): 749-757. https://doi.org/10.12677/AAM.2018.77090

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