Abstract
In this paper, we propose a functional fittings-stage Runge-Kutta method which is based on the exact integration of the set of the linearly independent functions φi(t), (i = 1,...,s). The method is exact when the solution of the ODE can be expressed as the linear combination of φi(t), although the method has an error for general ODE. In this work we investigate the order of accuracy of the method for general ODEs, and show that the order of accuracy of the method is at leasts, if the functions φi(t) are sufficiently smooth and the method is non-confluent. Furthermore, it is shown that the attainable order of the method is 2s, like conventional Runge-Kutta methods. Two- and three-stage methods including embedded one of this type are developed.
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Ozawa, K. A functional fitting Runge-Kutta method with variable coefficients. Japan J. Indust. Appl. Math. 18, 107–130 (2001). https://doi.org/10.1007/BF03167357
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DOI: https://doi.org/10.1007/BF03167357