New embedded explicit pairs of exponentially fitted Runge-Kutta methods

DOI10.1016/j.cam.2010.01.041zbMath1189.65144OpenAlexW2086281006MaRDI QIDQ966090

B. E. Eshmatov

Publication date: 27 April 2010

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.2010.01.041

zbMATH Keywords

periodic solutionsnumerical examplesRunge-Kutta methodsexponential fittingoscillatory IVPs

Mathematics Subject Classification ID

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

Related Items (6)

Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮ On the numerical stability of the exponentially fitted methods for first order IVPs ⋮ Numerical solution of reaction-diffusion systems of \(\lambda\)-\(\omega\) type by trigonometrically fitted methods ⋮ On modified Runge-Kutta trees and methods ⋮ Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations ⋮ NEURAL NETWORK-BASED DERIVATION OF EFFICIENT HIGH-ORDER RUNGE–KUTTA–NYSTRÖM PAIRS FOR THE INTEGRATION OF ORBITS

Cites Work

• Structure preservation of exponentially fitted Runge-Kutta methods
• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• A family of embedded Runge-Kutta formulae
• High order embedded Runge-Kutta formulae
• Runge-Kutta algorithms for oscillatory problems
• Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
• Explicit methods based on a class of four stage fourth order Runge-Kutta methods for preserving quadratic laws
• Frequency evaluation in exponential fitting multistep algorithms for ODEs
• Global error estimation with Runge-Kutta triples
• Exponentially fitted Runge-Kutta methods
• An embedded pair of exponentially fitted explicit Runge-Kutta methods
• Exponentially-fitted explicit Runge-Kutta methods
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Solving Ordinary Differential Equations I
• On the Preservation of Invariants by Explicit Runge--Kutta Methods
• Interpolants for Runge-Kutta formulas

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