Superstable implicit Runge-Kutta methods for second order initial value problems |
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Authors: | R. K. Jain Rajive Kumar Rakesh Goel |
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Affiliation: | (1) Department of Mathematics, Indian Institute of Technology, 110016 Hauz Khas, New Delhi, India;(2) India Meteorological Department, Lodi Road, 110003 New Delhi, India |
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Abstract: | Using the well known properties of thes-stage implicit Runge-Kutta methods for first order differential equations, single step methods of arbitrary order can be obtained for the direct integration of the general second order initial value problemsy=f(x, y, y),y(xo)=yo,y(xo)=yo. These methods when applied to the test equationy+2y+2y=0, ,0, +>0, are superstable with the exception of a finite number of isolated values ofh. These methods can be successfully used for solving singular perturbation problems for which f/y and/or f/y are negative and large. Numerical results demonstrate the efficiency of these methods. |
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Keywords: | AMS(MOS): 65L05 |
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