Numerical Solutions of Ordinary Fractional Differential Equations with Singularities

被引：2

作者：

Dimitrov, Yuri ^{[1
]}

Dimov, Ivan ^{[2
,3
]}

Todorov, Venelin ^{[2
,3
,4
]}

机构：

[1] Univ Forestry, Dept Math & Phys, Sofia 1756, Bulgaria

[2] Bulgarian Acad Sci, Inst Informat & Commun Technol, Sofia, Bulgaria

[3] Dept Parallel Algorithms, Acad Georgi Bonchev Str,Block 25 A, Sofia 1113, Bulgaria

[4] Bulgarian Acad Sci, Inst Math & Informat, Dept Informat Modeling, Acad Georgi Bonchev Str,Block 8, BU-1113 Sofia, Bulgaria

来源：

ADVANCED COMPUTING IN INDUSTRIAL MATHEMATICS (BGSIAM 2017) | 2019年 / 793卷

关键词：

DIFFUSION; SCHEME;

D O I：

10.1007/978-3-319-97277-0_7

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of the numerical solutions of FDEs whose solutions are differentiable functions. In the present paper we propose a method for improving the accuracy of the numerical solutions of ordinary linear FDEs with constant coefficients which uses the fractional Taylor polynomials of the solutions. The numerical solutions of the two-term and three-term FDEs are studied in the paper.

引用

页码：77 / 91

页数：15

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