Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels
Abstract
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work with an approximate solution for all previous points in time. In this paper, the considered nonlocal problem is transformed into a local one; a loosely coupled equation system with additional ordinary differential equations is solved. This approach is based on the approximation of the difference kernel by the sum of exponentials. Estimates for the stability of the solution concerning the initial data and the righthand side for the corresponding Cauchy problem are obtained. Twolevel schemes with weights with convenient computational implementation are constructed and investigated. The theoretical consideration is supplemented by the results of the numerical solution of the integrodifferential equation when the kernel is the stretching exponential function.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.15125
 Bibcode:
 2021arXiv211015125V
 Keywords:

 Mathematics  Numerical Analysis;
 34K30;
 35R20;
 47G20;
 65J08;
 65M12
 EPrint:
 15 pages, 5 figures