﻿ 应用RKM和ADM分解方法解一类二阶积分微分方程 RKM and ADM Decomposition Method for Solving a Class of Two-Order Integral-Differential Equations

Pure Mathematics
Vol.06 No.01(2016), Article ID:16856,7 pages
10.12677/PM.2016.61010

RKM and ADM Decomposition Method for Solving a Class of Two-Order Integral-Differential Equations

Xuejiao Lian, Xueqin Lv

Harbin Normal University, Harbin Heilongjiang

Received: Jan. 6th, 2016; accepted: Jan. 25th, 2016; published: Jan. 29th, 2016

ABSTRACT

In this paper, we use RKM and ADM decomposition method to solve a class of second-order boundary value problems for integral-differential equations. This method avoids the series solution of the equation with unknown parameters. At the same time, the problem of convergence analysis is also given in this paper. Additionally, some numerical examples are presented to demonstrate the rationality of this algorithm.

Keywords:Two-Order Integral-Differential Equations, Reproducing Kernel Method, ADM Decomposition Method, Convergence Analysis

1. 引言

(1.1)

。 (1.2)

(1.3)

(1.4)

(1.5)

(1.6)

(1.7)

(1.8)

(1.9)

(1.10)

(1.11)

2. 新的方法

(2.1)

(2.2)

(2.3)

，再生核定义为

(2.4)

(2.5)

(2.6)

(2.7)

(2.8)

(2.9)

(2.10)

(2.11)

(2.12)

(2.13)

(2.14)

(2.15)

(2.16)

(2.16)给出了方程(1.3)的最终形式，次截断得到的级数解为

。 (2.17)

3. 收敛性分析

(3.1)

。 (3.2)

，(3.3)

， (3.4)

， (3.5)

(3.6)

， (3.7)

4. 数值算例

(4.1)

(4.2)

(4.3)

Table 1. Comparison of the absolute error of Example 4.1 by using new method and modified ADM decomposition method in the paper [7]

5. 结论

RKM and ADM Decomposition Method for Solving a Class of Two-Order Integral-Differential Equations[J]. 理论数学, 2016, 06(01): 65-71. http://dx.doi.org/10.12677/PM.2016.61010

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