NINTH ORDER BLOCK PIECEWISE CONTINUOUS HYBRID INTEGRATORS FOR SOLVING SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This paper presents a Piecewise Continuous Hybrid Integrator (PCHI) of order nine that has the ability to produce continuous solution defined for all values of the required independent variable. The PCHI is used to generate several implicit   hybrid integrators that are expressed in block form and are applied as a Block Hybrid Integrators (BHI) for the numerical solution    of second order initial value problems at both grid and off-grid points. The stability properties of the method are discussed.

Numerical examples are given to illustrate the accuracy and efficiency of the proposed BHI.