On parallel solution of ordinary differential equations

TL;DR

This paper compares the performance of a parallel iterated Runge-Kutta method with serial methods for solving ODEs, introduces a new fully parallelized stepsize estimation algorithm, and demonstrates its superior performance on large systems.

Contribution

It presents a novel fully parallelized stepsize estimation algorithm that outperforms existing methods, especially for large systems of ODEs.

Findings

Parallel method has comparable runtime to serial methods but uses more resources.

New parallel stepsize estimation algorithm outperforms traditional methods.

Significant efficiency gains in large system integrations.

Abstract

In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is comparable to that of the serial versions, thought it uses considerably more computational resources. A new algorithm is proposed where full parallelization is used to estimate the best stepsize for integration. It is shown that this new method outperforms the others, notably, in the integration of very large systems.