A Class of New Block Generalized Adams Implicit Runge-Kutta Collocation Methods

Abstract

In this paper, the reformulation of the block generalized Adams methods into block generalized Adams implicit Rung-Kutta methods for step numbers k =3, 4, 5, is considered. This is because of the usefulness of block implicit Runge-Kutta methods for the solution of stiff ordinary differential equations. The new methods proposed in this paper turn out to be A-stable and possess the stability properties of the Runge-Kutta methods and have implicit structure for accurate and efficient implementation. Numerical examples obtained demonstrate the accuracy and efficiency of the new block methods.