Haar wavelet method for solving differential equations

Abstract

Haar wavelet method has become an efficient tool for solving various types of integral and differential equations. In this thesis, we apply Haar wavelet method to solve certain second order ordinary differential equations with initial and boundary conditions and we find the general form for solve of second order linear ordinary differ- ential equations by Haar wavelet method. Moreover, we extend the interval of second order ordinary differential equation's solutions from [0, 1] to [r, r + 1] when r is an in- teger. Finally, we look into conditions for solve of the Black-Scholes equation by Haar wavelet method.