Combined nonstandard numerical methods for ODEs with polynomial right-hand sides

Benito M. Chen-Charpentier, Dobromir T. Dimitrov and Hristo V. Kojouharov

Mathematics and Computers in Simulation (MATCOM), 2006, vol. 73, issue 1, 105-113

Abstract: In this paper we formulate conditions that guarantee second-order accuracy of the one-step nonstandard finite difference methods for general first order autonomous ordinary differential equations. We also develop a new class of nonstandard finite-difference methods for differential equations of the form dx/dt=polynomial(x), based on earlier results obtained in reference [H.V. Kojouharov, B.M. Chen, Nonstandard Eulerian–Lagrangian methods for multi-dimensional reactive transport problems, Appl. Numer. Math. 49 (2) (2004) 225–243]. Error analysis and numerical examples that demonstrate the performance of the proposed new method are also provided.

Keywords: Finite difference; Nonstandard scheme; Exact methods; Autonomous dynamical systems (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:73:y:2006:i:1:p:105-113

DOI: 10.1016/j.matcom.2006.06.008

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