Superconvergence of numerical solutions to Volterra integral equations with singularities

被引：23
作者：
Hu, QY [1 ]
机构：
[1] CHINESE ACAD SCI,MATH INST,BEIJING 100080,PEOPLES R CHINA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 1997年 / 34卷 / 05期
关键词：
weakly singular integral equation; beta-derivative; beta-polynomial discrete collocation; corrected quasi-graded meshes; higher-order interpolation; superconvergence;
D O I：
10.1137/S0036142994266832
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we discuss the beta-polynomial discrete collocation method (based on practical meshes) for Volterra integral equations with weakly singular kernels. It will be shown that superconvergence properties may be obtained by using appropriate collocation parameters and by a simple, cheap postprocessing of the original discrete collocation solution.
引用
收藏
页码：1698 / 1707
页数：10
相关论文
共 7 条
[1]   NONPOLYNOMIAL SPLINE COLLOCATION FOR VOLTERRA-EQUATIONS WITH WEAKLY SINGULAR KERNELS [J].
BRUNNER, H .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (06) :1106-1119
[2]   POLYNOMIAL SPLINE COLLOCATION METHODS FOR VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS [J].
BRUNNER, H .
IMA JOURNAL OF NUMERICAL ANALYSIS, 1986, 6 (02) :221-239
[3]  
BRUNNER H, 1985, MATH COMPUT, V45, P417, DOI 10.1090/S0025-5718-1985-0804933-3
[4]  
GRAHAM IG, 1982, MATH COMPUT, V37, P95
[5]   Stieltjes derivatives and beta-polynomial spline collocation for Volterra integrodifferential equations with singularities [J].
Hu, QY .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1996, 33 (01) :208-220
[6]   SUPERCONVERGENCE OF NUMERICAL-SOLUTIONS TO WEAKLY SINGULAR VOLTERRA INTEGRODIFFERENTIAL EQUATIONS [J].
TANG, T .
NUMERISCHE MATHEMATIK, 1992, 61 (03) :373-382
[7]   A NOTE ON COLLOCATION METHODS FOR VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS [J].
TANG, T .
IMA JOURNAL OF NUMERICAL ANALYSIS, 1993, 13 (01) :93-99
1