Numerical solutions for Volterra integro-differential forms of Lane-Emden equations of first and second kind using Legendre multi-wavelets

Abstract

A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved by any numerical method. Illustrative examples are discussed to show the validity and applicability of the present method.

Keywords

• Legendre multi-wavelet
• Volterra integral equation
• integro-differential equation
• Lane-Emden equation