Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations

DOI10.1016/j.apnum.2019.03.006zbMath1477.65110OpenAlexW2931382864MaRDI QIDQ2311792

Yanyan Li

Publication date: 4 July 2019

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2019.03.006

zbMATH Keywords

B-seriestrigonometrical fittingorder conditionNyström treeperiodicity regiontwo-derivative Runge-Kutta-Nyström method

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (2)

Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems ⋮ Adaptive multi-step Runge-Kutta-Nyström methods for general second-order ordinary differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems
• On explicit two-derivative Runge-Kutta methods
• Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations
• Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
• Comparing different ODE modelling approaches for gene regulatory networks
• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• Limit-cycle-preserving simulation of gene regulatory oscillators
• Dynamic patterns of gene regulation. I: Simple two-gene systems
• New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation
• Order conditions for RKN methods solving general second-order oscillatory systems
• Trigonometrically fitted two-derivative Runge-Kutta methods for solving oscillatory differential equations
• New methods for oscillatory systems based on ARKN methods
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Solving Ordinary Differential Equations I
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• On modified TDRKN methods for second-order systems of differential equations
• A New Theoretical Approach to Runge–Kutta Methods
• P-stability and exponential-fitting methods for y = f(x,y)
• Structure-Preserving Algorithms for Oscillatory Differential Equations
• Geometric Numerical Integration
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

This page was built for publication: Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations