Limit-cycle-preserving simulation of gene regulatory oscillators
type: Item
instance of: scholarly article
title: Limit-cycle-preserving simulation of gene regulatory oscillators
zbMATH Open document ID: 1257.92026
DOI: 10.1155/2012/673296
author: Xiong You
published in: Discrete Dynamics in Nature and Society
publication date: 2013-02-21T00:00:00Z
review text: Summary: In order to simulate gene regulatory oscillators more effectively, Runge-Kutta (RK) integrators are adapted to the limit-cycle structure of the system. Taking into account the oscillatory features of gene regulatory oscillators, phase-fitted and amplification-fitted Runge-Kutta (FRK) methods are designed. New FRK methods with phase-fitted and amplification-fitted updates are also considered. The error coefficients and error constants for each of the new FRK methods are obtained. In the numerical simulations of the two-gene regulatory system, the new methods are shown to be more accurate and more efficient than their prototype RK methods in the long-term integration. It is a new discovery that the best fitting frequency not only depends on the problem to be solved, but also depends on the method.
Mathematics Subject Classification ID: 92C42
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65C20
zbMATH DE Number: 6137747
Wikidata QID: Q58700698
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/673296
OpenAlex ID: W2144440382
cites work: Comparing different ODE modelling approaches for gene regulatory networks
cites work: Numerical Methods for Ordinary Differential Equations
cites work: Runge-Kutta methods: Some historical notes
cites work: Solving Ordinary Differential Equations I
cites work: Numerical integration of products of Fourier and ordinary polynomials
cites work: Numerical integration of ordinary differential equations based on trigonometric polynomials
cites work: Multistep Numerical Methods Based on the Scheifele G-Functions with Application to Satellite Dynamics
cites work: A four-step phase-fitted method for the numerical integration of second order initial-value problems
cites work: Runge-Kutta algorithms for oscillatory problems
cites work: Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
cites work: Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
cites work: Runge-Kutta methods adapted to the numerical integration of oscillatory problems
cites work: Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems
cites work: Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators
cites work: Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
cites work: A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems
cites work: An exponentially-fitted high order method for long-term integration of periodic initial-value problems
cites work: Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
cites work: An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems
cites work: Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
cites work: A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
cites work: Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)
cites work: Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
cites work: An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
cites work: Exponentially fitted Runge-Kutta methods
cites work: Optimal implicit exponentially-fitted Runge-Kutta methods
cites work: Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods
cites work: Frequency evaluation in exponential fitting multistep algorithms for ODEs
cites work: Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
cites work: Frequency evaluation for exponentially fitted Runge-Kutta methods
cites work: On the frequency choice in trigonometrically fitted methods
description: scientific article; zbMATH DE number 6137747