Extended Runge-Kutta-like formulae

DOI10.1016/j.apnum.2005.11.008zbMath1104.65075OpenAlexW2049257286MaRDI QIDQ850189

Xin-Yuan Wu, Jian-Lin Xia

Publication date: 15 November 2006

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2005.11.008

zbMATH Keywords

absolute stabilityerror estimatesnumerical examplesstepsize controltwo-step Runge-Kutta methodextended Runge-Kutta-like method

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (10)

Parameter estimations of fuzzy forced Duffing equation: numerical performances by the extended Runge-Kutta method ⋮ Numerical solutions of fuzzy differential equations by an efficient Runge-Kutta method with generalized differentiability ⋮ Linear matrix differential dynamical systems with fuzzy matrices ⋮ Numerical solutions of fuzzy differential equations by extended Runge-Kutta-like formulae of order 4 ⋮ On explicit two-derivative two-step Runge-Kutta methods ⋮ Derivation of three-derivative Runge-Kutta methods ⋮ Analysis of the parametric models of passive scalar transport used in the lattice Boltzmann method ⋮ Optimized low-dispersion and low-dissipation two-derivative Runge-Kutta method for wave equations ⋮ Exponentially fitted two-derivative DIRK methods for oscillatory differential equations ⋮ New two-derivative implicit-explicit Runge-Kutta methods for stiff reaction-diffusion systems

Uses Software

• ATOMFT

Cites Work

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• ATOMFT: Solving ODEs and DAEs using Taylor series
• Runge-Kutta with higher order derivative approximations
• A sixth-order \(A\)-stable explicit one-step method for stiff systems
• Stiffly stable second derivative multistep methods with higher order and improved stability regions
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• Some general implicit processes for the numerical solution of differential equations
• The automatic integration of ordinary differential equations
• On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

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