基于半正交B样条小波的第二类分数阶Fredholm积分方程数值解法  

Numerical solution of the second kind of fractional Fredholm integral equation based on semi-orthogonal B-spline wavelet

作　　者：闫洁 韩惠丽 周春梅[1] 白龙[1] YAN Jie;HAN Hui-li;ZHOU Chun-mei;BAI Long(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan 756099,Ningxia,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756099

出　　处：《西北师范大学学报（自然科学版）》2023年第2期12-17,共6页Journal of Northwest Normal University(Natural Science)

基　　金：宁夏自然科学基金资助项目(2021AAC03028,2022AAC03332,2022AAC03333);宁夏高等学校科学研究项目(NYG2022074);宁夏高等学校一流学科建设(教育学学科)项目(NXYLXK2021B10)。

摘　　要：采用半正交B样条小波方法将第二类线性分数阶Fredholm积分方程的核函数、已知函数和未知函数展开,给出收敛性定理及误差分析;结合选取的等距配置点将积分方程转化为线性代数方程组进行求解;通过数值算例验证了方法的有效性.The kernel function,known function and unknown function of the second kind of linear fractional Fredholm integral equation are expanded by using the semi-orthogonal B-spline wavelet method,and the convergence theorem and error analysis are given.Combined with the selected equidistant collocation points,the integral equation is transformed into system of linear algebraic equations.Finally,the effectiveness of this method is verified by numerical examples.

关 键 词：第二类FREDHOLM积分方程 半正交B样条小波 分数阶微积分 配置法 

分 类 号：O175.5[理学—数学]