Spline Collocation for Fractional Integro-Differential Equations

被引：4
|
作者：
Pedas, Arvet [1 ]
Tamme, Enn [1 ]
Vikerpuur, Mikk [1 ]
机构：
[1] Univ Tartu, Inst Math, EE-50409 Tartu, Estonia
来源：
Finite Difference Methods, Theory and Applications | 2015年 / 9045卷
关键词：
BOUNDARY-VALUE-PROBLEMS; PIECEWISE POLYNOMIAL COLLOCATION; DIFFERENTIAL-EQUATIONS; NUMERICAL-METHODS; ORDER;
D O I：
10.1007/978-3-319-20239-6_34
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We consider a class of boundary value problems for fractional integro-differential equations. Using an integral equation reformulation of the boundary value problem, we first study the regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the boundary value problem by suitable non-polynomial approximations is discussed. Optimal global convergence estimates are derived and a super-convergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.
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页码：315 / 322
页数：8
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