## NUMERICAL SOLUTION OF NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS USING HAAR WAVELET COLLOCATION METHOD

Published: 2016-11-08

Page: 99-109

S. C. SHIRALASHETTI *

Department of Studies in Mathematics, Karnatak University, Dharwad-580003, India

Department of Studies in Mathematics, Karnatak University, Dharwad-580003, India

*Author to whom correspondence should be addressed.

### Abstract

In the present work, Haar wavelet collocation method for the numerical solution of nonlinear volterra integro-differential equations is proposed. Properties of Haar wavelet and its operational matrix are utilized to convert the integro-differential equation into a system of algebraic equations. The required Haar coefficients are computed using Matlab. The technique is tested on two simple pedagogic examples and comparisons are made with the exact and existing method. Error analysis is worked out, which shows efficiency of the method.

Keywords: Haar wavelet collocation method (HWCM), operational matrix, adomian decomposition method (ADM), nonlinear volterra integro-differential equations

#### How to Cite

SHIRALASHETTI, S. C., & MUNDEWADI, R. A. (2016). NUMERICAL SOLUTION OF NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS USING HAAR WAVELET COLLOCATION METHOD. Asian Journal of Mathematics and Computer Research, 14(2), 99–109. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/679