Numerical solution of third-order boundary value problems by using a two-step hybrid block method with a fourth derivative

Abstract

This article proposes a two-step hybrid block method (TSHBM) with a fourth derivative for solving third-order boundary value problems in ordinary differential equations. The mathematical formulation of the proposed approach depends on interpolation and collocation techniques. The order of convergence of the TSHBM is showed to be seventh-order convergent and zero-stable. A few numerical examples are given to evaluate its performance. Numerical outcomes show that the TSHBM scheme is more efficient than some existing numerical techniques.