Local Linearization Method for Numerical Integration of Delay Differential Equations

In this paper, a new approach for the numerical computation of delay differential equations (DDEs) is introduced. The essential idea consists of obtaining numerical integrators that use a code expressly developed for linear DDEs, in contrast with the conventional approach of using a code for ordinary differential equations. Specifically, two numerical schemes of this new class of integrators are proposed and their numerical viability analyzed. It includes the estimation of the convergence rate, the evaluation of the computational cost of the schemes, and a simulation study. It is proved that these one-step explicit integrators converge uniformly with order two to the solution of nonlinear DDEs and are able to integrate stiff equations in a satisfactory way with low computational cost.

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