1. Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions.
- Author
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Wang, Yu-Lan, Du, Ming-Jing, Temuer, Chao-Lu, and Tian, Dan
- Subjects
REPRODUCING kernel (Mathematics) ,PARTIAL differential equations ,CAPUTO fractional derivatives ,ORDINARY differential equations ,PIECEWISE linear approximation ,FRACTIONAL integrals - Abstract
Today, most of the real physical world problems can be best modelled with fractional telegraph equation. Besides modelling, the solution techniques and their reliability are the most important. Therefore, high accuracy solutions are always needed. As we all know, reproducing kernel method (RKM) has been successfully presented for solving various ordinary differential equations. However, the numerical results are not perfectly satisfactory when we directly use the traditional RKM for solving fractional partial differential equation. The aim of this paper is to fill this gap. In this paper, a new method is provided for solving fractional telegraph equation in the reproducing kernel space by piecewise technique, which can obtain more accurate solution than traditional method. Three experiments are given to demonstrate the effectiveness of the present method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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