Second derivative general linear methods with inherent Runge-Kutta stability

DOI10.1007/s11075-016-0099-6zbMath1351.65051OpenAlexW2253904156MaRDI QIDQ329310

A. Movahedinejad, Ali Abdi, Gholamreza Hojjati

Publication date: 21 October 2016

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

Full work available at URL: https://doi.org/10.1007/s11075-016-0099-6

zbMATH Keywords

numerical experiments\(A\)-stabilitystiff differential equationsvariable stepsizesecond derivative methods\(L\)-stabilityinherent Runge-Kutta stability

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical methods for stiff equations (65L04)

Related Items (12)

Efficient Nordsieck second derivative general linear methods: construction and implementation ⋮ Global error estimation for explicit second derivative general linear methods ⋮ EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ⋮ Symmetric second derivative integration methods ⋮ RK-stable second derivative multistage methods with strong stability preserving based on Taylor series conditions ⋮ Strong stability-preserving three-derivative Runge-Kutta methods ⋮ Implementation of second derivative general linear methods ⋮ Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs ⋮ Efficient second derivative methods with extended stability regions for non-stiff IVPs ⋮ Projection of second derivative methods for ordinary differential equations with invariants ⋮ Partitioned second derivative methods for separable Hamiltonian problems ⋮ CONSTRUCTION OF NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS WITH INHERENT QUADRATIC STABILITY

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