On a family of trigonometrically fitted extended backward differentiation formulas for stiff and oscillatory initial value problems

DOI10.1007/s11075-016-0148-1zbMath1355.65089OpenAlexW2394704231MaRDI QIDQ503368

Yong-Cai Geng, Sumit K. Garg

Publication date: 12 January 2017

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-016-0148-1

zbMATH Keywords

stabilitynumerical exampleserror analysisblock methodsoscillatory initial value problemstrigonometrically fitted extended backward differentiation formula

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 (6)

Adapted block hybrid method for the numerical solution of Duffing equations and related problems ⋮ One step adapted hybrid second derivative block method for initial value problems with oscillating solutions ⋮ A family of boundary value methods for systems of second-order boundary value problems ⋮ A second-derivative functionally fitted method of maximal order for oscillatory initial value problems ⋮ Boundary value methods for second-order PDEs via the Lanczos-Chebyshev reduction technique ⋮ Exponential and trigonometrical fittings: user-friendly expressions for the coefficients

Uses Software

• DIFSUB

Cites Work

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• A robust trigonometrically fitted embedded pair for perturbed oscillators
• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae
• Explicit, high-order Runge-Kutta-Nyström methods for parallel computers
• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• Trigonometrically fitted block Numerov type method for \(y = f(x, y, y')\)
• Block hybrid method using trigonometric basis for initial value problems with oscillating solutions
• Analysis of trigonometric implicit Runge-Kutta methods
• A functionally fitted three-stage explicit singly diagonally implicit Runge-Kutta method
• Block methods for second order odes
• P-stability and exponential-fitting methods for y = f(x,y)
• Block Implicit One-Step Methods
• A Runge-Kutta for all Seasons
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
• A special stability problem for linear multistep methods
• Optimal implicit exponentially-fitted Runge-Kutta methods

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