Some generalized two-step block hybrid Numerov method for solving general second order ordinary differential equations without predictors

Abstract

This paper proposes a class of generalized two-step Numerov methods, a block hybrid type for the direct solution of general second order ordinary differential equations. Both the main method and additional methods were derived via interpolation and collocation procedures. The basic properties of zero stability, consistency and convergence of these methods were also investigated. Results from numerical examples show significant improvement.

Keywords: Block Hybrid Methods, Ordinary Differential Equations, Continuous formulation, Interpolation and Collocation, Numerov method