第一类弱奇异核Fredholm积分方程的数值求解  

A Numerical Solution of Weakly Singular Fredholm Integral Equation of First Kind

作　　者：闵涛[1] 胡刚[1] 晏立刚 

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《应用泛函分析学报》2014年第2期167-171,共5页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金重大项目(51190093);国家自然科学基金(50979088;51179151)

摘　　要：第一类弱奇异核Fredholm积分方程由于奇异及本质的不适定性,给求解带来很大难度.本文首先利用克雷斯变换将方程转化,并对转化后的方程进行高斯-勒让德离散,得到一离散不适定的线性方程组,结合正则化方法对该类问题进行数值求解。最后给出了数值模拟,验证了本文方法的可行性及有效性.Beacause the weakly singular Fredholm integral equation of first kind the nature of the singularity and ill-posedness, so solving is great difficulty. Then we firstly transform the equation into by Kress, and ransformed equations and Gauss-Legendre discrete, and we get the not be a discrete set of linear equations. Regularization method with the class of the numerical solution of the problem. Finally, a numerical simulation verify the feasibility and effectiveness.

关 键 词：FREDHOLM积分方程 正则化 克雷斯变换 高斯-勒让德离散 

分 类 号：O241.83[理学—计算数学]