Error of partitioned Runge-Kutta methods for multiple stiff singular perturbation problems
This paper considers the error behaviour of partitioned Runge-Kutta methods (PRKs) applied to stiff singular perturbation problems where the stiffness arises through the size of the reciprocal of the perturbation parameter. Under certain assumptions which include algebraic stability and diagonal stability and with \(q\) the minimum of the stage orders of the two component methods in the PRK formulation then the global orders are shown to be \(q\) in both the stepsize and the perturbation parameter.
scientific article; zbMATH DE number 1437132