Abstract
Simulation of large networks of chemical reactions via the numerical integration of large systems of ordinary differential equations is of growing importance in real-world problems. We propose an attractive novel numerical integration method, that is largely independent from ill-conditioning and is suitable for any nonlinear problem; moreover, the method, being exact for linear problems, is especially precise for quasi-linear problems, the most frequent kind in the real world. The method is based on a new approach to the computation of a matrix exponential, includes an automatic correction of rounding errors, is not too expensive computationally, and lends itself to a short and robust software implementation that can be easily inserted in large simulation packages. A preliminary numerical verification has been performed, with encouraging results, on two sample problems. The full source listing (in standard C language) of an academic version of the algorithm is freely available on request (e-mail address: Valerio.Parisi@roma2.infn.it), together with a very simple but very stiff chemical problem.
Published Version
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