Analysis of trigonometric implicit Runge–Kutta methods |
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Authors: | Hoang Si Nguyen Roger B Sidje Nguyen Huu Cong |
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Institution: | 1. Faculty of Mathematics-Mechanics-Informatics, College of Sciences, Vietnam National University, Hanoi, Vietnam;2. Advanced Computational Modelling Centre, Department of Mathematics, University of Queensland, Brisbane QLD 4072, Australia;3. School of Graduate Studies, Vietnam National University, Hanoi, Vietnam |
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Abstract: | Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge–Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge–Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. |
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Keywords: | Oscillatory ODEs Variable stepsize Variable coefficients Trigonometric collocation Implicit RK |
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