Functionally fitted explicit two step peer methods. (English) Zbl 1326.65090
Summary: In this paper we study functionally fitted methods based on explicit two step peer formulas. We show that with \(s\) stages it is possible to get explicit fitted methods for fitting spaces of high dimension \(2s\), by proving the existence and uniqueness of such formulas. Then, we obtain particular methods with \(2\) and \(3\) stages fitted to trigonometric and exponential spaces of dimension \(4\) and \(6\), respectively. By means of several numerical examples we show the performance of the obtained methods, comparing them to fitted Adams-Bashforth-Moulton methods with the same order.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
peer methods; exponential fitting; periodic problems; numerical example; Adams-Bashforth-Moulton methodReferences:
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