Fourth-order symmetric DIRK methods for periodic stiff problems

DOI10.1023/A:1024077930017zbMath1058.65072OpenAlexW2024861657MaRDI QIDQ1397934

D. Massart

Publication date: 6 August 2003

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

Full work available at URL: https://doi.org/10.1023/a:1024077930017

zbMATH Keywords

numerical examplessymplectic methodsdispersion errordiagonally implicit Runge-Kutta method\(P\)-stabilitysymmetric DIRK 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) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (10)

Exponentially fitted symmetric and symplectic DIRK methods for oscillatory Hamiltonian systems ⋮ Two novel classes of linear high-order structure-preserving schemes for the generalized nonlinear Schrödinger equation ⋮ Novel high-order energy-preserving diagonally implicit Runge-Kutta schemes for nonlinear Hamiltonian ODEs ⋮ High-order Lagrange multiplier method for the coupled Klein-Gordon-Schrödinger system ⋮ Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations ⋮ Phase error analysis of implicit Runge-Kutta methods: new classes of minimal dissipation low dispersion high order schemes ⋮ A numerical evaluation of solvers for the periodic Riccati differential equation ⋮ Accuracy and linear stability of RKN methods for solving second-order stiff problems ⋮ Linear high-order energy-preserving schemes for the nonlinear Schrödinger equation with wave operator using the scalar auxiliary variable approach ⋮ Exponentially fitted two-derivative DIRK methods for oscillatory differential equations

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