Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators

You, Xiong; Zhang, Yonghui; Zhao, Jinxi

doi:10.1016/j.cpc.2011.04.001

Cited by 22 publications

(5 citation statements)

References 20 publications

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“…These methods have the important property of integrating harmonic oscillations as a fixed frequency without truncation error. A new method TFSTS (Trigonometrically-Fitted Scheifele Two-Step), based on the Scheifele methods, which verifies this property has been published in [9].…”

Section: Introductionmentioning

confidence: 84%

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Cortés-Molina¹,

García-Alonso²,

Reyes³

2019

JAMP

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Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J 2 .

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Section: Introductionmentioning

confidence: 84%

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Cortés-Molina¹,

García-Alonso²,

Reyes³

2019

JAMP

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“…Geometric numerical integration aims at solving differential equations effectively while preserving the geometric properties of the exact flow [ 14 ]. Recently, You et al [ 15 ] develop a family of trigonometrically fitted Scheifele two-step (TFSTS) methods, derive a set of necessary and sufficient conditions for TFSTS methods to be of up to order five based on the linear operator theory, and construct two practical methods of algebraic four and five, respectively. Very recently, You [ 16 ] develops a new family of phase-fitted and amplification methods of Runge-Kutta type which have been proved very effective for genetic regulatory networks with a limit-cycle structure.…”

Section: Introductionmentioning

confidence: 99%

Splitting Strategy for Simulating Genetic Regulatory Networks

You

Liu

Musa

2014

Computational and Mathematical Methods in Medicine

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The splitting approach is developed for the numerical simulation of genetic regulatory networks with a stable steady-state structure. The numerical results of the simulation of a one-gene network, a two-gene network, and a p53-mdm2 network show that the new splitting methods constructed in this paper are remarkably more effective and more suitable for long-term computation with large steps than the traditional general-purpose Runge-Kutta methods. The new methods have no restriction on the choice of stepsize due to their infinitely large stability regions.

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“…Their methods are shown to be more efficient than the codes in the literature for some typical test problems and for the Lotka-Volterra system and a twogene regulatory network in biology as well. You et al [18] investigated the trigonometrically fitted Scheifele methods for oscillatory problems. A good theoretical foundation of the exponential fitting techniques for multistep methods was presented by Gautschi [19] and Lyche [20].…”

Section: Introductionmentioning

confidence: 99%

A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems

Zhang

Che

Fang

et al. 2013

Journal of Applied Mathematics

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A new trigonometrically fitted fifth-order two-derivative Runge-Kutta method with variable nodes is developed for the numerical solution of the radial Schrödinger equation and related oscillatory problems. Linear stability and phase properties of the new method are examined. Numerical results are reported to show the robustness and competence of the new method compared with some highly efficient methods in the recent literature.

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Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators

Cited by 22 publications

References 20 publications

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Splitting Strategy for Simulating Genetic Regulatory Networks

A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems

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