Explicit two-derivative Runge-Kutta methods coupled with Richardson Extrapolation
Mozjgan Eghbaljoo, Gholamreza Hojjati, Ali Abdi, Pari Khakzad
Statistics and Computer Science, University of Tabriz, Tabriz, Iran
Keywords: ordinary differential equations, second derivative methods, Runge-Kutta methods, Richardson extrapolation, stability properties, accuracy
Abstract
The aim of this paper is to derive efficient numerical algorithms for the numerical solution of nonstiff ordinary differential equations by applying the Richardson extrapolation technique to a class of explicit two-derivative Runge-Kutta methods. Theoretical results illustrate that the application of this technique has considerable impact on the accuracy and stability properties of the underlying numerical methods. The achieved improvements of the proposed algorithms are also confirmed by the results of some numerical experiments.
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