首页
>
期刊首页
>
计算数学（英文版）
>
2026年6期
>
ON THE SUPERCONVERGENCE OF COLLOCATION METHODS BASED ON TWO POST-PROCESSING TECHNIQUES FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS
ON THE SUPERCONVERGENCE OF COLLOCATION METHODS BASED ON TWO POST-PROCESSING TECHNIQUES FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS
摘要
The purpose of this paper is to investigate the superconvergence of collocation meth-ods for fractional integro-differential equations(FIDEs)with weakly singular kernels and Caputo derivative of order 0＜α＜1.First,the initial value problem of FIDEs is reformu-lated as a weakly singular Volterra integral equation(VIE),and the existence,uniqueness,and regularity of the exact solution for the original FIDE are obtained with the help of the resolvent theory of VIEs,and it is shown that the singularity of the exact solution is governed by the Caputo derivative,not the weakly singular kernel.Next,the piecewise polynomial collocation method is employed to solve the reformulated VIE numerically,and the optimal convergence order of the collocation solution is obtained on graded meshes.In order to improve the numerical accuracy,two types of postprocessing techniques are used-one is the classical iterated technique for VIEs and another one is the interpolation postprocessing technique.The superconvergence is thoroughly investigated and the opti-mal superconvergence orders are obtained for both of these two postprocessing techniques.Compared to the classical iterated collocation method,the interpolation postprocessing method has a lower calculation cost.The theoretical results are illustrated by numerical experiments.
年，卷(期)：
2026, 44(6)
分类号：
65L05
65L20
65L50
机标分类号：
O241
H146.2
V435
在线出版日期：
2026年9月15日
