Three Stage Inverse Implicit Runge–Kutta Scheme for Solution of Ordinary Differential Equations

Abstract

This paper describes the Development, Analysis and Implementation of Three-Stage Inverse Implicit Runge–Kutta Schemes for Treatment Ordinary Differential Equations. Its development adopts Taylor series expansion to generate its parameters.  The analysis of its basics properties adopted Dalhquist A–stable model test equation and theoretical results show that the method is A–stable, P-stable, consistent and convergent.  Numerical results and comparative analysis with existing method show that the method is accurate and effective.

Keywords: A–stable, P–stable, effective, accurate, inverse, convergent, consistent.