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Multivalue collocation methods free from order reduction. (English) Zbl 1458.65073

Summary: This paper introduces multivalue collocation methods for the numerical solution of stiff problems. The presented approach does not exhibit the phenomenon of order reduction, typical of collocation based Runge-Kutta methods applied to stiff systems, since the introduced methods have uniform effective order of convergence on the overall integration interval. Examples of methods as well as numerical experiments on a selection of stiff problems are given.

MSC:

65L04 Numerical methods for stiff equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations

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