A 3-step fourth derivatives method for numerical integration of third order ordinary differential equations

Abstract

A 3-Step Hybrid Block Method (S3HBM) with three mid-step grid points based on Linear Multistep Method is presented in this work for direct approximation of solution of third-order Initial and Boundary Value Problems (IVPs and BVPs). Multiple Finite Difference formulas are derived using the collocation technique. These formulas are unified in a block formulation to form a numerical integrator that solves general third-order ordinary differential equations. Basic properties of the derived method are discussed. The superiority of this method over existing methods is established numerically on different test problems, to show its better performance in terms od accuracy.