Chebyshev wavelet method for numerical solutions of integro-differential form of Lane-Emden type differential equations

摘要

In this paper, Chebyshev wavelet method (CWM) has been applied to solve the second-order singular differential equations of Lane-Emden type. Firstly, the singular differential equation has been converted to Volterra integro-differential equation and then solved by the CWM. The properties of Chebyshev wavelets were first presented. The properties of Chebyshev wavelets via Gauss-Legendre rule were used to reduce the integral equations to a system of algebraic equations which can be solved numerically by Newton's method. Convergence analysis of CWM has been discussed. Illustrative examples have been provided to demonstrate the validity and applicability of the present method.