Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems

DOI10.1155/2013/136961zbMath1275.65042OpenAlexW2169654348WikidataQ58915340 ScholiaQ58915340MaRDI QIDQ369713

Norazak Senu, Sufia Zulfa Ahmad, Fudziah Bt. Ismail, Mohamed Bin Suleiman

Publication date: 19 September 2013

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/136961

zbMATH Keywords

numerical resultsabsolute stabilityperiodicitydispersion order sixoscillatory second-order ordinary differential equationsRunge-Kutta Nyström methodthree-stage fifth-orderthree-stage fourth-ordertwo-step semi-implicit hybrid methodszero dissipation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (3)

Zero-dissipative semi-implicit hybrid method for solving oscillatory or periodic problems ⋮ Solving oscillatory delay differential equations using block hybrid methods ⋮ A four-stage fifth-order trigonometrically fitted semi-implicit hybrid method for solving second-order delay differential equations

Cites Work

• Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
• A phase-fitted Runge-Kutta-Nyström method for the numerical solution of initial value problems with oscillating solutions
• A symplectic Runge-Kutta-Nyström method with minimal phase-lag
• A note on a diagonally implicit Runge-Kutta-Nyström method
• An explicit hybrid method of Numerov type for second-order periodic initial-value problems
• An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
• An invariant imbedding algorithm for the solution of inhomogeneous linear two-point boundary value problems
• An efficient implicit Runge-Kutta method for second order systems
• Stabilization of Cowell's method
• 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
• High-accuracy P-stable Methods for y^″ = f(t, y)
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• A one-step method for direct integration of structural dynamic equations
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Order conditions for a class of two-step methods for y = f (x, y)
• Numerical Methods for Ordinary Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems