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On the solution of stiff ordinary differential equations. (English) Zbl 1178.65081

Todorov, Michail D. (ed.), Applications of mathematics in engineering and economics ’34. Proceedings of the 34th international conference (AMEE ’08), Sozopol, Bulgaria, 8–14 June 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0598-1/hbk). AIP Conference Proceedings 1067, 442-447 (2008).
Summary: We consider a new method based on simplex integrals for stiff ordinary differential equations. In contrast to the Kuntzmann-Butcher method [E. Hairer, S. P. Nørsett and G. Wanner, Solving ordinary differential equations. I: Nonstiff problems. 2. rev. ed. Springer Series in Computational Mathematics. 8. Berlin: Springer-Verlag (1993; Zbl 0789.65048)], this method requires the solution of less simultaneous implicit equations. Numerical examples illustrate the efficiency of this technique.
For the entire collection see [Zbl 1165.82004].

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations

Citations:

Zbl 0789.65048
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