An Efficient 4-Step Block Method for Solution of First Order Initial Value Problems Via Shifted Chebyshev Polynomial

Isah I. O., Salawu, A. S., Olayemi, K. S. and Enesi. L. O.
Keywords: Interpolation, Collocation, Block method, Zero-stability, Convergence
Tropical Journal of Science and Technology 2020 1(2), 25-36. Published: March 10, 2021


Abstract

In this paper, we develop a four-step block method for solution of first order initial value problems of ordinary differential equations. The collocation and interpolation approach is adopted to obtain a continuous scheme for the derived method via Shifted Chebyshev Polynomials, truncated after sufficient terms. The properties of the proposed scheme such as order, zero-stability, consistency and convergence are also investigated. The derived scheme is implemented to obtain numerical solutions of some test problems, the result shows that the new scheme competes favorably with exact solution and some existing methods.