The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
B-convergence of Lobatto IIIC formulas
Numerische Mathematik
On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
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In this paper, we present some results on the error behavior of variable stepsize stiffly-accurate Runge-Kutta 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 Runge-Kutta methods which are not algebraically stable or diagonally stable. Some results on the existence and uniqueness of the solution of Runge-Kutta equations are also presented.