We derive exponentially fitted two-step Runge-Kutta methods for the numerical solution of y' = f(x,y), specially tuned to the behaviour of the solution. Such methods have nonconstant coefficients which depend on a parameter to be suitably estimated. The construction of the methods is shown and a strategy of parameter selection is presented. Some numerical experiments are provided to confirm the theoretical expectations.
Exponentially fitted two-step Runge-Kutta methods: Construction and parameter selection
D'AMBROSIO, RAFFAELE;PATERNOSTER, Beatrice
2012-01-01
Abstract
We derive exponentially fitted two-step Runge-Kutta methods for the numerical solution of y' = f(x,y), specially tuned to the behaviour of the solution. Such methods have nonconstant coefficients which depend on a parameter to be suitably estimated. The construction of the methods is shown and a strategy of parameter selection is presented. Some numerical experiments are provided to confirm the theoretical expectations.File in questo prodotto:
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