A Parallel Fourth Order Rosenbrock Method: Construction, Analysis and Numerical Comparison

Abstract

The present paper sheds some light on constructing a new fourth order, four-stage parallel Rosenbrock method (NPROS4) and investigating its convergence and stability properties in view of solving stiff ordinary differential equations. The expression for local truncation error (LTE) has been derived and the parameters are chosen to minimize the coefficients in the LTE term. It is pertinent to point out here that this method possesses more free parameters to improve the stability region. The present method can also be efficiently implemented in a parallel computer having four processors with less error than the existing methods of the same order. Numerical examples are given to illustrate the efficiency of the present developed method.