Trigonometrically-fitted ARKN methods for perturbed oscillators☆
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Cited by (43)
The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods
2023, Journal of Computational and Applied MathematicsCitation Excerpt :Multi-frequency ERKN methods have been widely used in many fields of science and engineering. They have been investigated for exponentially or trigonometrically fitted methods [2,4,10–12] and for two-step hybrid methods [13] solving oscillatory second-order differential equations, for energy-preserving methods [14] solving multi-frequency oscillatory Hamiltonian systems, for asymptotic methods solving highly oscillatory problems [15,16], for symplectic methods solving Hamiltonian ODEs [5,17–20], and for multisymplectic methods solving Hamiltonian PDEs [21]. The purpose of this section is to simplify the symplectic conditions for ERKN methods.
An approach to solving Maxwell's equations in time domain
2023, Journal of Mathematical Analysis and ApplicationsCitation Excerpt :Then, effective solvers for ODEs can be used. Typically, the solvers mean some effective integrators appeared in the literature, such as the Gautschi-type method [7], trigonometric Fourier collocation methods [34], extended Runge-Kutta(-Nystrom) methods [38,46,48–51,53,54], and the discrete energy-preserving methods (the AVF methods) [4,20–23,28,30,45]. All of them can be carried by replacing the differential operator by a suitable differentiation matrix in the operator-variation-of-constants formula for Maxwell's equations.
A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting
2021, Applied Numerical MathematicsA novel class of explicit divergence-free time-domain methods for efficiently solving Maxwell's equations
2021, Computer Physics CommunicationsSymplectic and symmetric trigonometrically-fitted ARKN methods
2019, Applied Numerical MathematicsCitation Excerpt :For more work we see [16,17,26]. Recently, in order to let ARKN methods behave better in integrating oscillatory problems (1), Yang et al. [28] modified the ARKN methods by introducing frequency depending coefficients into the terms in the internal stages and proposed trigonometrically-fitted ARKN (TFARKN) methods. Numerical tests of [28] have shown the superiority of these methods.
A new analytical formula for the wave equations with variable coefficients
2018, Applied Mathematics Letters
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