B-convergence of general linear methods for stiff problems Original Research Article

This paper is concerned with the numerical solution of stiff initial value problems for systems of ordinary differential equations by general linear methods. We prove that algebraic stability together with strict stability at infinity implies B-convergence for strictly dissipative systems and that the order of B-convergence of a method is equal to the generalized stage order, where the generalized stage order is not less than the stage order, which extends the relevant results on Runge–Kutta methods. As applications of this result, B-convergence results of some classes of multistep Runge–Kutta methods are obtained.