An efficient wavelet based approximation method for a few second order differential equations arising in science and engineering

Abstract— A new wavelet based approximation method for solving the second order differential equations arising science and engineering is presented in this paper. Such differential equation is often applied to model phenomena in various fields of science and engineering. In this study, shifted second kind Chebyshev wavelet (CW) operational matrices of derivatives is introduced and applied for solving the second order differential equations with various initial conditions. The key idea for getting the numerical solutions for these equations is to convert the differential equations (linear or nonlinear) to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Some illustrative examples are given to demonstrate the validity and applicability of the proposed method. The power of the manageable method is confirmed. Moreover the use of the shifted second kind Chebyshev wavelet method (CWM) is found to be simple, flexible, efficient, small computation costs and computationally attractive.