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Wavelet Galerkin solutions of ordinary differential equations. (English) Zbl 1236.65084

Summary: Advantage of wavelet Galerkin method over finite difference or element method has led to tremendous applications in science and engineering. In recent years there has been increasing attempt to find solutions of differential equations using wavelet techniques. In this paper, we elaborate the wavelet techniques and apply Galerkin procedure to analyse one dimensional harmonic wave equation as a test problem using fictitious boundary approach; overcoming L.U. Dianfeng et al. [Treatment of boundary condition in the application of wavelet-Galerkin method to a SH wave problem, Akita Univ. (1996)] reservation at higher resolution. This could have been possible only after evaluating connection coefficients at various scales.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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