Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method

Advances in Difference Equations

Atefeh Fahim¹  Jalil Rashidinia¹  Mohammad Ali Fariborzi Araghi¹  Mehdi Jalalvand² 

[1] Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran;School of Mathematics, Iran University of Science and Technology, Tehran, Iran

关键词: partial integro-differential equation;    sinc-collocation method;    finite difference method;    product trapezoidal integration rule;    65R99;    45A99;    45K05;   

DOI  :  10.1186/s13662-017-1416-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We provide the numerical solution of a Volterra integro-differential equation of parabolic type with memory term subject to initial boundary value conditions. Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc-collocation method is employed in space. A weakly singular kernel has been viewed as an important case in this study. The convergence analysis has been discussed in detail, which shows that the approach exponentially converges to the solution. Furthermore, numerical examples and illustrations are presented to prove the validity of the suggested method.

【 授权许可】

CC BY