Numerical technique for higher-order differential equation with variable coefficients via Haar wavelet method

Abstract

Lately, Haar wavelet has been established as a mathematical implement for several problems. In this article, the numerical method is founded on operational matrices and Haar wavelet collocation points on a new-found interval [0, Ω]. For a chosen domain from 0 to Ω, we have established the method of integration the Haar wavelets functions. The operational matrices of integration and product are used to change the higher order differential equations containing variable coefficients into system of algebraic equations that can be solved via MATLAB. Three numerical cases have be presented which including higher order linear differential equations involving variable coefficients. The numerical solution completely converge in comparison with accurate results.

Subject Classification:

• 65L03
• 31A35

Keywords:

• Numerical method
• Higher order differential equations including variable coefficients
• Haar wavelet
• Haar wavelet operation matrices