Stability of ROW methods for non autonomous systems of ordinary differential equations

Abstract

AN-stability of ROW methods is studied. The concept of LN-equivalent schemes belonging to different classes of one-step methods is introduced to do it. Ways to construct ROW methods with improved stability for linear nonautonomous and nonlinear problems are studied using the algebraic stability of singly diagonally implicit Runge-Kutta (SDIRK) methods. The existing SDIRK methods are shown to be inapplicable to construct LN-stable ROW methods for numerical integration of stiff systems of ordinary differential equations.