Local linearization-runge kutta (LLRK) methods for solving ordinary differential equations

Authors:
H. De la Cruz;R. J. Biscay;F. Carbonell;J. C. Jimenez;T. Ozaki
Affiliations:
Universidad de Granma, Bayamo, MN, Cuba;Instituto de Cibernética, Matemática y Física, La Habana, Cuba;Instituto de Cibernética, Matemática y Física, La Habana, Cuba;Instituto de Cibernética, Matemática y Física, La Habana, Cuba;Institute of Statistical Mathematics, Tokyo, Japan
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Year:
2006

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Abstract

A new class of stable methods for solving ordinary differential equations (ODEs) is introduced. This is based on combining the Local Linearization (LL) integrator with other extant discretization methods. For this, an auxiliary ODE is solved to determine a correction term that is added to the LL approximation. In particular, combining the LL method with (explicit) Runge Kutta integrators yields what we call LLRK methods. This permits to improve the order of convergence of the LL method without loss of its stability properties. The performance of the proposed integrators is illustrated through computer simulations.