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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.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Tsitouras, Ch: Explicit two-step methods for second-order linear ivps. Computers math. Applic. 43, No. 8/9, 943-949 (2002) · Zbl 1050.65071
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