Implicit Runge-Kutta Method for Van Der Pol Problem
Applied and Computational Mathematics
Volume 4, Issue 1-1, January 2015, Pages: 6-11
Received: Jun. 7, 2014; Accepted: Jun. 25, 2014; Published: Jul. 13, 2014
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Authors
Jafar Biazar, Department of Applied Mathematics, Faculty of Mathematical sciences, University of Guilan, P.O Box: 41635-19141, Rasht, Iran
Meysam Navidyan, Department of Applied Mathematics, Faculty of Mathematical sciences, University of Guilan, P.O Box: 41635-19141, Rasht, Iran
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Abstract
In this manuscript the implicit Runge-Kutta (IRK) method, with three slopes of order five has been explained, and is applied to Van der pol stiff differential equation. Truncation error, of order five, has been estimated. Stability of the procedure for the Van der pol equation, is analyzed by the Lyapunov method. To illustrate the structure of the method, an Algorithm is presented to solve this stiff problem. Results confirm the validity and the ability of this approach.
Keywords
Implicit Method, Taylor Series, Legendre Orthogonal Polynomial, Van Der Pol Equation, Lyapunov Function
To cite this article
Jafar Biazar, Meysam Navidyan, Implicit Runge-Kutta Method for Van Der Pol Problem, Applied and Computational Mathematics. Special Issue: New Orientations in Applied and Computational Mathematics. Vol. 4, No. 1-1, 2015, pp. 6-11. doi: 10.11648/j.acm.s.2015040101.12
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