Accelerated Solution of High Order Non-linear ODEs using Chebyshev Spectral Method Comparing with Adomian Decomposition Method

In this article, an accurate Chebyshev spectral method for solving high order non-linear ODEs is presented. Properties of the Chebyshev polynomials are utilized to reduce the computation of the problem to a set of algebraic equations. Some examples are given to verify and illustrate the efficiency and simplicity of the method. We compared our numerical results against the Adomian decomposition method (ADM). Special attention is given to study the convergence analysis of ADM. Numerical results were obtained from these two methods show that the proposed techniques are in excellent conformance in most cases. Also, from the presented examples, we found that the proposed method can be applied to wide class of high order non-linear ODEs.