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An application of single-term Haar wavelet series in the solution of nonlinear oscillator equations. (English) Zbl 1162.65040

Summary: A novel single-term Haar wavelet series (STHWS) method is implemented for the solution of the Duffing equation and Painlevé’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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
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