DEVELOPMENT OF A CONTINUOUS MULTI-STEPONE-FOURTH STEP HYBRID SCHEME FOR THIRD-ORDERIVP IN ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This study introduces a hybrid block approach for the approximate solution of initial value problems involving third-order ordinary differential equations. The formulation of the method employs orthogonal and  Chebyshev polynomials as basis functions, with its performance enhanced through the incorporation of off-step points. This modification is aimed at achieving zero-stability while maintaining high computational accuracy. Several numerical experiments are carried out to demonstrate the methods effectiveness, and the results confirm its reliability and efficiency in solving such problems.