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Trigonometric fitted modification of RADAU5
Author(s) -
Medvedeva Marina A.,
Simos Theodore E.,
Tsitouras Charalampos
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5986
Subject(s) - mathematics , trigonometry , initial value problem , perturbation (astronomy) , runge–kutta methods , trigonometric series , calculus (dental) , mathematical analysis , numerical analysis , medicine , dentistry , physics , quantum mechanics
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.