Technical Report 12, c4e-Preprint Series, Cambridge

A New Explicit Numerical Scheme For Large and Stiff Systems of Ordinary Differential Equations

ref: Technical Report 12, c4e-Preprint Series, Cambridge

Associated Theme: Numerics

Abstract

This paper introduces a new explicit numerical method with adaptive time stepping which is suited to large and stiff systems of ordinary differential equations (ODEs). The algorithm, which is motivated by the theory of Markov jump processes, is very simple and can be easily programmed. Various numerical experiments are performed to assess the efficiency of the algorithm. For this the ignition of a stoichiometric mixture of n-decane and air at constant pressure and temperature is modelled using a large system of ordinary differential equations containing 1218 strongly coupled and stiff equations. The new algorithm is compared to the software packages DASSL and LSODE, which are shown to be outperformed for moderate precision. The numerical experiments also indicates that the approximate solution obtained from the new algorithm converges to the exact solution of the ODE.

Material from this preprint has been published in: Combustion Theory and Modelling 10 (1), 171-182, (2006)

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