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Numerical solution of typical initial value problems using haar wavelet transform method

Author: 
Shiralashetti, S. C. and Kantli, M. H.
Subject Area: 
Physical Sciences and Engineering
Abstract: 

Wavelet analysis is a recently developed mathematical tool for many problems. In this paper, we apply Haar wavelet transform method to solve typical Initial value problems. Numerical examples are shown which including first, second, higher order differential equations with constant and variable coefficients, singular non-linear initial value problems. The results show that the haar wavelet transform method is quite reasonable when compare to R. K. Method and exact. R. K. Methods they are distinguished by their orders in the sense that they agree with Taylor’s series solution up to terms of hr, where r is the order of the method. These methods do not demand prior computation of higher derivatives of y(t) as in Taylor’s series method. Fourth-order Runge –Kutta methods are widely used for finding the numerical solutions of linear or non-linear ordinary differential equations, the development of which is complicated algebraically. Also, Numerical accuracy of the R. K. Method is not quite good as compared to exact and haar wavelet transforms method in case of higher order and typical initial value problems.

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