非线性分数阶Fredholm积分方程的B样条小波解法  

The Numerical Solution of Nonlinear Fractional-Order Fredholm Integral Equation by B-Spline Wavelet Collocation Method

作　　者：闫洁 韩慧丽 陆万顺[1] 马旭[1] YAN Jie;HAN Huili;LU Wanshun;MA Xu(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan Ningxia 756000,China;School of Mathematics Statistics Science,Ningxia University,Yinchuan Ningxia 750021,China)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756000 [2]宁夏大学数学统计学院,宁夏银川750021

出　　处：《江西师范大学学报（自然科学版）》2020年第6期604-608,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(1126104111762016);宁夏高等学校科学研究课题(NGY2018-137);宁夏高等学校一流学科建设(教育学学科)(NXYLXK2017B11);宁夏师范学院校级科研课题(NXSFZDC1803)资助项目.

摘　　要：利用B样条小波函数数值求解非线性分数阶第2类Fredholm积分方程,将具有紧支集的线性半正交B样条尺度函数和小波函数一起应用于数值求解非线性分数阶第2类Fredholm积分方程中.这种方法将非线性分数阶Fredholm积分方程转化为非线性代数方程组,再通过数值求解方程组得到原方程的数值解,证明了误差边界值,数值算例验证了本方法的有效性和准确性.The semiorthogonal B-spline wavelet are used to solve the solution of fractional-order Fredholm integral equation of the second kind.Compactly supported linear semiorthogonal B-spline scaling functions and wavelet functions are applied to approximate the solutions of nonlinear fractional-order Fredholm integral equation of the second kind.This method reduces the nonlinear fractional-order Fredholm integral equation to a nonlinear system of algebraic equations,numerical solution of original equation is obtained through solving algebraic equations and error bound value is estimated.Finally,some examples demonstrate the validity and precision of this method.

关 键 词：分数阶微积分 B样条小波 FREDHOLM积分方程 配置法 

分 类 号：O175.5[理学—数学]