Trigonometric fitted modification of RADAU5 |
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| Authors: | Marina A Medvedeva Theodore E Simos Charalampos Tsitouras |
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| Institution: | 1. Ural Federal University, Mira 19, Yekaterinburg, Russia;2. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11541 Saudi Arabia;3. General Department, National and Kapodistrian University of Athens, Euripus Campus, 34400 Greece |
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| Abstract: | Implicit Runge-Kutta (RK) methods are in common use when addressing stiff initial value problems (IVP). They usually share the property of A-stability that is of crucial importance in solving the latter type of IVP. Radau IIA family of implicit RK methods is among the preferred ones. Especially its fifth-order representative named RADAU5 has received a lot of attention for use with lax accuracies. Here, we try the lesser possible perturbation of its coefficients. Then, we derive a trigonometric fitted modification that is intended to be applied in periodic IVPs. Numerical tests over a variety of problems with oscillatory solutions justify our effort. |
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| Keywords: | implicit Runge-Kutta initial value problems stiff oscillatory solutions variable coefficients |
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