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Title: Optimum runge-kutta-fehlberg methods for second-order differential equations
Authors: Jain R.K.
Jain, Manoj Kumar
Published in: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Abstract: The optimum Runge-Kutta method of a particular order is the one whose truncation error is minimum. In this paper, we have derived optimum Runge-Kutta mehtods of 0(hm+4), 0(hm+5) and 0(hm+6) for m = 0(1)8, which can be directly used for solving the second order differential equation yn = f(x, y, y'). These methods are based on a transformation similar to that of Fehlberg and require two, three and four evaluations of f(x, y, y') respectively, for each step. The numercial solutions of one example obtained with these methods are given. It has been assumed that f(x, y, y')is sufficiently differentiable in the entire region of integration. © 1972 by Academic Press Inc. (London) Limited.
Citation: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) (1972), 10(2): 202-210
Issue Date: 1972
ISSN: 2724960
Author Scopus IDs: 26659438700
Author Affiliations: Jain, R.K., Mathematics Department, University of Saskatchewan, Saskatoon, Canada
Jain, M.K., Mathematics Department, Indian Institute of Technology, New Delhi, India
Corresponding Author: Jain, R.K.; Deparment of Mathematics, Indian Institute of Technology, Madras, India
Appears in Collections:Journal Publications [HY]

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