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Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations

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Computational Science – ICCS 2006 (ICCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3991))

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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.

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© 2006 Springer-Verlag Berlin Heidelberg

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De la Cruz, H., Biscay, R.J., Carbonell, F., Jimenez, J.C., Ozaki, T. (2006). Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_22

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