Optimum Runge-Kutta-Fehlberg Methods for Second-order Differential Equations |
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Authors: | JAIN, R. K. JAIN, M. K. |
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Affiliation: | 1Mathematics Department, University of Saskatchewan Saskatoon, Canada 2Mathematics Department, Indian Institute of Technology New Delhi, India |
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Abstract: | * Presently at Deparment of Mathematics, Indian Institute of Technology, Madras, India. The optimum Runge-Kutta method of a particular order is theone whose truncation error is minimum. In this paper, we havederived optimum Runge-Kutta mehtods of 0(hm+4), 0(hm+5) and0(hm+6) for m = 0(1)8, which can be directly used for solvingthe second order differential equation yn = f(x, y, y'). Thesemethods are based on a transformation similar to that of Fehlbergand require two, three and four evaluations of f(x, y, y') respectively,for each step. The numercial solutions of one example obtainedwith these methods are given. It has been assumed that f(x,y, y')is sufficiently differentiable in the entire region ofintegration. |
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