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An application of single-term Haar wavelet series in the solution of nonlinear oscillator equations

✍ Scribed by N.M. Bujurke; S.C. Shiralashetti; C.S. Salimath

Book ID
104005852
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
546 KB
Volume
227
Category
Article
ISSN
0377-0427

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✦ Synopsis

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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✍ Marija MiloΕ‘eviΔ‡; Miljana JovanoviΔ‡ πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 282 KB

The subject of this paper is the analytic approximation method for solving stochastic differential equations with time-dependent delay. Approximate equations are defined on equidistant partitions of the time interval, and their coefficients are Taylor approximations of the coefficients of the initia