Magnus integrators for linear and quasilinear delay differential equations

TL;DR

This paper introduces a numerical method using Magnus integrators and spectral discretization to solve linear and certain quasilinear delay differential equations with high accuracy, especially in periodic cases.

Contribution

It presents a novel Magnus expansion-based algorithm for efficiently solving non-autonomous linear delay differential equations and extends it to some quasilinear cases.

Findings

Accurate computation of characteristic multipliers in periodic delay equations

Effective spectral discretization of delay terms

Extension to specific quasilinear delay equations

Abstract

A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary differential equation which is subsequently solved with numerical integrators obtained from the Magnus expansion. The algorithm can be used in the periodic case to get both accurate approximations of the characteristic multipliers and the solution itself. In addition, it can be extended to deal with certain quasilinear delay equations.