Application of LegendreWavelets for Solving Ordinary Differential Equations
Ajay
Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur-273009, India.
Jitendra Kumar Kushwaha *
Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur-273009, India.
Rishi Nath Mishra
Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur-273009, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, an efficient and accurate method has been developed for solving linear differential equations. A polynomial function f (t) is approximated over the interval [0,1]. In the proposed procedure, the operational matrix of integration based on Legendre wavelets has been employed. The approximate as well as exact solution of differential equation has been determined by Legendre wavelet technique. The analytical and graphical solution of given differential equation has been classified in the work. The proposed technique effectively shows the comparison of exact and approximate solution of differential equation. The solution found by this method is more accurate and very close to the exact solution. Present work gives a new technique for finding the solution of certain differential equations in [0,1). Therefore it is very useful for coming researchers.
Keywords: Legendre polynomials, Legendre wavelet, wavelet approximation, operational matrix of integration, absolute error