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Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution. (English) Zbl 1062.65075
Summary: A dissipative trigonometrically-fitted two-step explicit hybrid method is constructed. This method is based on a dissipative explicit two-step method developed recently by {\it C. Tsitouras} [Comput. Math. Appl. 43, No. 8--9, 943--949 (2002; Zbl 1050.65071)]. Numerical examples show that the procedure of trigonometrical fitting is an efficient way for one to produce numerical methods for the solution of second-order linear initial value problems (IVPs) with oscillating solutions.

##### MSC:
 65L06 Multistep, Runge-Kutta, and extrapolation methods 65L05 Initial value problems for ODE (numerical methods) 34A34 Nonlinear ODE and systems, general
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##### References:
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