Error analysis of variable stepsize RungeKutta methods for a class of multiply-stiff singular perturbation problems ?
In this paper, we present some results on the error behavior of variable stepsize stiffly-accurate RungeKutta methods applied to a class of multiply-stiff initial value problems of ordinary differential equations in singular perturbation form, under some weak assumptions on the coefficients of the considered methods. It is shown that the obtained convergence results hold for stiffly-accurate RungeKutta methods which are not algebraically stable or diagonally stable. Some results on the existence and uniqueness of the solution of RungeKutta equations are also presented.
error variable stepsize rungekutta methods singular perturbation problems multiple-stiffness