Functionally fitted Runge-Kutta-Nyström methods

2014/10/16 by N. S. Hoang, Hoang, N. S., Roger B. Sidje +1
Mathematics · Engineering · Computer Science · #Numerical methods for differential equations #Electromagnetic Simulation and Numerical Methods #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1410.4287

Abstract

We have shown previously that functionally fitted Runge-Kutta (FRK) methods can be studied using a convenient collocation framework. Here, we extend that framework to functionally fitted Runge-Kutta-Nyström (FRKN) methods, shedding further light on the fact that these methods can integrate a second-order differential equation exactly if its solution is a combination of certain basis functions, and that superconvergence can be obtained when the collocation points satisfy some orthogonality conditions. An analysis of their stability is also conducted.

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