Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems

DOI10.1016/j.cam.2016.09.016zbMath1357.65087OpenAlexW2520735905MaRDI QIDQ507888

Yanping Yang, Xiong You, Yong Lei Fang

Publication date: 9 February 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.09.016

zbMATH Keywords

stabilitynumerical experimentsphase-lagtruncation errorshighly oscillatory problemsequation dependent coefficienttrigonometrically fitted two-step hybrid methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

Symplectic and symmetric trigonometrically-fitted ARKN methods ⋮ Exponential fitting for interpolation of oscillatory functions. A numerical approach ⋮ A functionally-fitted block Numerov method for solving second-order initial-value problems with oscillatory solutions ⋮ Two-frequency trigonometrically-fitted and symmetric linear multi-step methods for second-order oscillators ⋮ Obrechkoff two-step method fitted with Fourier spectrum for undamped Duffing equation

Cites Work

• Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection
• Construction of the ef-based Runge-Kutta methods revisited
• Exponentially fitted two-step hybrid methods for \(y^{\prime\prime} = f(x,y)\)
• Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations
• Variable stepsize Störmer-Cowell methods
• VSVO multistep formulae adapted to perturbed second-order differential equations
• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
• An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems
• Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• Runge-Kutta methods adapted to the numerical integration of oscillatory problems
• Runge-Kutta method with equation dependent coefficients
• Exponentially-fitted explicit Runge-Kutta methods
• Revised exponentially fitted Runge-Kutta-Nyström methods
• A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions
• Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
• A class of explicit two-step hybrid methods for second-order IVPs
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Order conditions for a class of two-step methods for y = f (x, y)
• A family of A-stable Runge Kutta collocation methods of higher order for initial-value problems
• An exponentially-fitted high order method for long-term integration of periodic initial-value problems

This page was built for publication: Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems