The exponential trapezoidal method for semilinear integro-differential equations
Numerical Analysis
2024-03-12 v1 Numerical Analysis
Abstract
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point iteration, making its implementation straightforward. Second-order convergence in time is shown in an abstract Hilbert space framework under reasonable assumptions on the problem. Numerical experiments illustrate the proven order of convergence.
Cite
@article{arxiv.2403.05900,
title = {The exponential trapezoidal method for semilinear integro-differential equations},
author = {Alexander Ostermann and Nasrin Vaisi},
journal= {arXiv preprint arXiv:2403.05900},
year = {2024}
}