Numerical solution of initial value problems by rational interpolation method using Chebyshev polynomials

Abstract

In this research, a modified rational interpolation method for the numerical solution of initial value problem is presented. The proposed method is obtained by fitting the classical rational interpolation formula in Chebyshev polynomials leading to a new stability function and new scheme. Three numerical test problems are presented in other to test the efficiency of the proposed method. The numerical result for each test problem is compared with the exact solution. The approximate solutions are show competitiveness with the exact solutions of the ODEs throughout the solution interval.

Keywords and Phrases: Chebyshev polynomial, Rational Interpolation, Minimaxpolynomial, Initial Value Problems and Ordinary Differential Equations (ODEs)