DEVELOPMENT OF ADAMS BASHFORTH METHODS USING CHEBYSHEV POLYNOMIAL AS BASIS FUNCTION

Abstract

 The important fundamental properties of numerical methods for ordinary differential equations are investigated. This involves the derivation of Adam Bashforth method for k=2, 3, 4 and k=5, together with their continuous forms using Chebyshev polynomials as basis function. The formulas derived were also used to solve Initial Valued Problems (IVP). The results agree remarkably with those from the literature.