Adomian分解法求解二维非线性Fredholm积分方程  

Adomian decomposition method for solving two-dimensional nonlinear Fredholm integral equations

作　　者：牛红玲[1] 夏静[2] 余志先[3] 

机构地区：[1]河北民族师范学院数学与计算机系,河北承德067000 [2]装甲兵工程学院基础部,北京100072 [3]上海理工大学理学院,上海200093

出　　处：《兰州理工大学学报》2014年第5期160-163,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11101282)

摘　　要：为了求一类二维非线性Fredholm积分方程数值解,提出Adomian分解法.采用Adomian多项式代替二维非线性Fredholm积分方程的非线性项,进而得到Adomian级数解.证明所得级数解在一定条件下收敛于原方程的精确解,同时给出Adomian级数解与精确解的最大截断误差.数值算例验证方法的有效性和理论的正确性.In order to get the numerical solution of a class of two-dimensional nonlinear Fredholm integral equations,Adomian decomposition method（ADM）is presented in this paper.The nonlinear term of twodimensional nonlinear Fredholm integral equations is replaced by Adomian polynomial,so that the Adomian series solutions are obtained.It is proved that the obtained Adomian series solutions will converge to the exact solution of original equation on certain conditions.Meantime,the maximum absolute truncated errors between the Adomian series solution and exact solution is given out.Finally,it is verified by a numerical example that the method is effective and the theory is valid.

关 键 词：二维非线性Fredholm积分方程 ADOMIAN多项式 ADOMIAN分解法 收敛性分析 数值解 精确解 

分 类 号：O241.8[理学—计算数学]