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Z. Naturforsch. 66a, 620 – 624
(2011)
doi:10.5560/ZNA.2011-0036
A New Approach to Van der Pols Oscillator Problem
1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2 Chemical Engineering Department, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran
3 Ege University, Science Faculty, Department of Mathematics, 35100 Bornova Izmir, Turkey
4 Physics Department, Faculty of Science, Mansoura University, Mansoura, 35516 Egypt
5 Modern Textile Institute, Donghua University, 1882 Yanan Xilu Road, Shanghai 200051, China
Received March 7, 2011 / revised July 2, 2011
Reprint requests to: Y. K.; E-mail:
yasirmath@yahoo.com
In this paper, we will consider the Laplace decomposition method (LDM) for finding series solutions of nonlinear oscillator differential equations. The equations are Laplace transformed and the nonlinear terms are represented by Hes polynomials. The solutions are compared with the numerical (fourth-order Runge–Kutta) solution and the solution obtained by the Adomian decomposition method. The suggested algorithm is more efficient and easier to handle as compared to the numerical method. The results illustrate that LDM is an appropriate method in solving the highly nonlinear equations.
Key words: Laplace Decomposition Method; Oscillator Differential Equation; Hes Polynomials.