Abstract
In this research work, we focused on the application of the first kind Chebychev polynomials as basis functions for the numerical solution of first and second order ordinary differential equations. For this purpose, the variational iteration method (VIM) was adopted as an iterative scheme to generate the required approximate solutions. The VIM with the Chebychev polynomials was applied to some selected linear and nonlinear problems for experimentations, and the resulting numerical evidence shows that it is effective and accurate.
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