On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods
The authors introduce new iterative schemes (so called single-Newton schemes) to the solution of the implicit equations in the \(s\)-stage Lobatto IIIA methods and study the linear stability properties of these schemes. Especially the effective constructions for the three-stage, fourth-order and for the four-stage, sixth-order Lobatto IIIA are considered. Their stability regions approximate to the negative complex half-plane as the number of iterations increases. Numerical results for the three following problems are presented: the Oregonator, the Van der Pol oscillator and the CUSP problem. The authors compare their code with three well-known codes for the solution of stiff systems: EPISODE, STRIDE and RADAU5. Lobatto IIIA formulae with the new iterative schemes can be competitive with standard codes used in solving stiff systems.
scientific article; zbMATH DE number 1084094
scientific article