Special algorithm for the numerical solution of system of initial value problems for ordinary differential equations using block hybrid extended trapezoidal rule of second kind

Abstract

We develop self-starting family of three and five step continuous extended trapezoidal rule of second kind a block hybrid type (BHETR₂s) methods through interpolation and collocation procedure. The BHETR₂s methods are then used to produce multiple numerical integrators which are each of the same order and assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the ordinary differential equations. The stability properties of the methods were investigated and found to be consistent, zero-stable and hence convergent. The block integrators were tested on three numerical initial value problems of ODEs to show accuracy and efficiency.

Keywords: BhETR₂s, Zero-Stability, Convergence, General Linear Method, Collocation Method, Trapezoidal Rule, Ordinary Differential Equation