Qualitatively stability of nonstandard 2-stage explicit Runge-Kutta methods of order two

DOI10.1134/S0965542516020123zbMath1362.65075MaRDI QIDQ2630007

Muhammad Mehdizadeh Khalsaraei, Fayyaz Khodadosti

Publication date: 8 July 2016

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

stabilityordinary differential equationspositivityinitial value problemsnumerical resultstepsizetrapezoidal and midpoint rulesnonstandard Runge-Kutta methods

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) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Uses Software

• RODAS

Cites Work

• Positivity for explicit two-step methods in linear multistep and one-leg form
• Total variation diminishing nonstandard finite difference schemes for conservation laws
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
• The positivity of low-order explicit Runge-Kutta schemes applied in splitting methods.
• Contributions to the mathematics of the nonstandard finite difference method and applications
• Total-Variation-Diminishing Time Discretizations
• Monotonicity-Preserving Linear Multistep Methods
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