Numerical Solution of Fractional Integro-Differential Equations with Non-Local Boundary Conditions

被引：0

作者：

Pedas, Arvet ^{[1
]}

Tamme, Enn ^{[1
]}

Vikerpuur, Mikk ^{[1
]}

机构：

[1] Univ Tartu, Inst Math & Stat, J Liivi 2, EE-50409 Tartu, Estonia

来源：

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017) | 2018年 / 1978卷

关键词：

fractional integro-differential equation; nonlocal boundary condition; Caputo derivative; piecewise polynomial approximation; SPLINE COLLOCATION;

D O I：

10.1063/1.5043773

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Numerical solution of fractional linear integro-differential equations with non-local boundary conditions is considered. The problem is reformulated as a Volterra integral equation of the second kind with respect to the fractional derivative of the solution of the original problem. First, the smoothness of the exact solution is studied. On the basis of the obtained regularity properties, by using spline collocation techniques, an efficient method for the numerical solution of the problem is proposed. The convergence of the proposed algorithms is shown and a global super-convergence result is presented. A numerical illustration is also given.

引用

页数：4

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