Sequential second derivative general linear methods for stiff systems

zbMath1302.65163MaRDI QIDQ464524

Ali Karam Ezzeddine, Gholamreza Hojjati, Ali Abdi

Publication date: 27 October 2014

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

numerical examplesstiff systems\(A\)-stability\(L\)-stabilityRunge-Kutta stability conditionssecond derivative general linear methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for stiff equations (65L04)

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Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs ⋮ Efficient Nordsieck second derivative general linear methods: construction and implementation ⋮ HIGH ORDER EXPLICIT SECOND DERIVATIVE METHODS WITH STRONG STABILITY PROPERTIES BASED ON TAYLOR SERIES CONDITIONS ⋮ A Class of Methods with Optimal Stability Properties for the Numerical Solution of IVPs: Construction and Implementation ⋮ RK-stable second derivative multistage methods with strong stability preserving based on Taylor series conditions ⋮ 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 ⋮ Strong stability preserving second derivative diagonally implicit multistage integration methods ⋮ Strong stability preserving second derivative general linear methods ⋮ CONSTRUCTION OF NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS WITH INHERENT QUADRATIC STABILITY

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