An improved class of generalized Runge-Kutta methods for stiff problems. II: The separated system case (Q706739)

The present work is an extension of an earlier work of the authors [part I: Appl. Math. Comput. 130, No.~2--3, 537--560 (2002; Zbl 1032.65071)]. They generalize the methods applied earlier so that they can be applied to some non-autonomous scalar ordinary differential equations and systems obtaining linearly implicit \(A\)-stable and \(L\)-stable methods. It may be noted that these methods do not require Jacobian evaluations in their implementation. Numerical examples are given to show the effective performance of the new schemes.