A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems

DOI10.1007/BF03167523zbMath1306.65229MaRDI QIDQ2258347

Kazufumi Ozawa

Publication date: 3 March 2015

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

zbMATH Keywords

periodic initial value problemsRunge-Kutta-Nyström methodtrigonometric order

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

A new collocation formulation for the block Falkner-type methods with trigonometric coefficients for oscillatory second order ordinary differential equations, Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday, On functionally-fitted Runge-Kutta methods, Analysis of trigonometric implicit Runge-Kutta methods, Functionally-fitted block \( \theta \)-methods for ordinary differential equations, Exponential fitted Runge-Kutta methods of collocation type: Fixed or variable knot points?, A new family of phase-fitted and amplification-fitted Runge-Kutta type methods for oscillators, Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\), Functionally fitted explicit pseudo two-step Runge-Kutta methods, Mixed collocation methods for \(y=f(x,y)\), A functional fitting Runge-Kutta method with variable coefficients, Optimal implicit exponentially-fitted Runge-Kutta methods, A functional fitting Runge-Kutta-Nyström method with variable coefficients., Functionally-fitted block methods for ordinary differential equations, A functionally fitted three-stage explicit singly diagonally implicit Runge-Kutta method, New methods for oscillatory problems based on classical codes

Cites Work

• Unnamed Item
• Stability of collocation-based Runge-Kutta-Nyström methods
• A theory for Nyström methods
• Modified Runge-Kutta-Fehlberg methods for periodic initial-value problems
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Solving Ordinary Differential Equations I
• Phase-Lag Analysis of Implicit Runge–Kutta Methods
• Numerical Solution of Ordinary Differential Equations
• Comparing Numerical Methods for Ordinary Differential Equations