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.
Multivalue collocation methods free from order reduction
D'Ambrosio R.
;
2021-01-01
Abstract
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.File in questo prodotto:
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