Exponentially fitted and trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for solving \(y^{\prime \prime}(x) = f \left(x, y, y^\prime\right)\)

DOI10.1155/2018/7689854zbMath1427.65117OpenAlexW2891573783WikidataQ62630586 ScholiaQ62630586MaRDI QIDQ1721425

Tahani Salama Mohamed, Nik Mohd Asri Nik Long, Zarina Bibi Ibrahim, Norazak Senu

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/7689854

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Cites Work

• Unnamed Item
• Unnamed Item
• Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems
• Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations
• Trigonometrically-fitted ARKN methods for perturbed oscillators
• A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag
• A robust trigonometrically fitted embedded pair for perturbed oscillators
• Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations
• High order embedded Runge-Kutta formulae
• Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations \(y^{\prime \prime}(x) = f(x, y, y^\prime)\)
• An embedded pair of exponentially fitted explicit Runge-Kutta methods
• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• A new family of phase-fitted and amplification-fitted Runge-Kutta type methods for oscillators
• New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems
• Trigonometrically fitted two-derivative Runge-Kutta methods for solving oscillatory differential equations
• Multidimensional ARKN methods for general oscillatory second-order initial value problems
• A new sixth-order algorithm for general second order ordinary differential equations
• Second Order Differential Equations
• Families of three-stage third order Runge-Kutta-Nyström methods for y″ = f (x, y, y′)
• Families of Direct Fourth-Order Methods for the Numerical Solution of General Second-Order Initial-Value-Problems
• On modified TDRKN methods for second-order systems of differential equations
• A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation

This page was built for publication: Exponentially fitted and trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for solving \(y^{\prime \prime}(x) = f \left(x, y, y^\prime\right)\)