An application of single-term Haar wavelet series in the solution of nonlinear oscillator equations |
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Authors: | NM Bujurke SC Shiralashetti CS Salimath |
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Institution: | 1. Department of Mathematics, Karnatak University, Dharwad-580003, India;2. Department of Mathematics, S.D.M. College of Engineering & Technology, Dharwad-02, India |
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Abstract: | In this paper, a novel single-term Haar wavelet series (STHWS) method is implemented for the solution of the Duffing equation and Painleve’s transcendents (PI and PII). The results, in the form of a block pulse and a discrete solution, are presented. Unlike classical numerical schemes, the STHWS method has no restrictions on the coefficients of the Duffing equation as regards its solution. PI and PII are analysed as regards their solutions, up to nearest singularities (poles), using the STHWS. Also, an efficient computational implementation shows the remarkable features of wavelet based techniques. |
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Keywords: | STHWS Operational matrix Block pulse and discrete solutions Gill&rsquo s method Duffing equation Painleve&rsquo s transcendents |
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