Record number :
Title of article :
Runge–Kutta methods adapted to the numerical integration of oscillatory problems Original Research Article
Author/Authors :
Y.A Erlangga، نويسنده , , C Vuik، نويسنده , , C.W. Oosterlee، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2004
Pages :
From page :
To page :
Abstract :
New Runge–Kutta methods specially adapted to the numerical integration of IVPs with oscillatory solutions are obtained. The coefficients of these methods are frequency-dependent such that certain particular oscillatory solutions are computed exactly (without truncation errors). Based on the B-series theory and on the rooted trees we derive the necessary and sufficient order conditions for this class of RK methods. With the help of these order conditions we construct explicit methods (up to order 4) as well as pairs of embedded RK methods of orders 4 and 3. Some numerical examples show the excellent behaviour when they compete with classical RK methods.
Journal title :
Applied Numerical Mathematics
Serial Year :
Link To Document :