CAS小波法求高阶弱奇异非线性积分微分方程数值解  

CAS wavelet method for solving numerical solution of high order nonlinear integro-differential equation with weak singularity

作　　者：魏金侠[1] 单锐[1] 刘文[1] 靳飞[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《合肥工业大学学报（自然科学版）》2012年第9期1293-1296,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(50875230);河北省教育厅科学研究计划资助项目(2009159)

摘　　要：为了求高阶变系数且带有弱奇异积分核非线性Volterra-Fredholm积分微分方程的数值解,文章结合CAS小波的性质及block pulse函数,给出任意阶弱奇异积分的近似求积公式,同时也给出CAS小波的积分算子矩阵,进而可以化简所求非线性积分微分方程,将原问题转换为求非线性方程组的解,数值算例验证了该方法的有效性。In order to obtain the numerical solution of high order variable coefficients nonlinear Volter- ra-Fredholm integro-differential equation with weakly singular kernels, an approximate formula which solves the solution of arbitrary order weakly singular integral is given by combining the properties of CAS wavelet and block pulse functions. And an integral operational matrix of CAS wavelet is also ob- tained. Then the original problem of the equation is translated irito solving a nonlinear system of alge- braic equations through simplifying and dispersing the nonlinear integro-differential equation. The nu- merical example shows that the method is effective.

关 键 词：高阶变系数 弱奇异 非线性 积分微分方程 CAS小波 BLOCK pulse函数 算子矩阵 数值解 

分 类 号：O241.8[理学—计算数学]