Construction and implementation of highly stable two-step continuous methods for stiff differential systems

DOI10.1016/j.matcom.2011.01.005zbMath1220.65096OpenAlexW2084627419MaRDI QIDQ551468

Raffaele D'Ambrosio, Zdzisław Jackiewicz

Publication date: 20 July 2011

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2011.01.005

zbMATH Keywords

numerical experimentserror estimationstiff systems\(A\)-stabilityinitial-value problemslocal error estimationtwo-step Runge-Kutta methods\(L\)-stabilitytwo-step continuous methodsvariable stepsize implementation

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) Numerical methods for stiff equations (65L04)

Related Items

Construction and implementation of two-step continuous methods for Volterra integral equations, Variable stepsize multivalue collocation methods, Multistep collocation methods for Volterra integro-differential equations, Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection, Two-step diagonally-implicit collocation based methods for Volterra integral equations, Two-step modified collocation methods with structured coefficient matrices, Perturbed MEBDF methods, Numerical integration of Hamiltonian problems by G-symplectic methods, Multivalue collocation methods free from order reduction, Order conditions for general linear Nyström methods, Parallel methods for weakly singular Volterra integral equations on GPUs, Search for efficient general linear methods for ordinary differential equations, \(P\)-stable general Nyström methods for \(y=f(y(t))\), Exponentially fitted singly diagonally implicit Runge-Kutta methods, GPU-acceleration of waveform relaxation methods for large differential systems, A family of matrix coefficient formulas for solving ordinary differential equations, Multivalue second derivative collocation methods, Nested second derivative two-step Runge-Kutta methods

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two-step modified collocation methods with structured coefficient matrices
• Two-step Runge-Kutta methods with quadratic stability functions
• Error estimators for stiff differential equations
• Two-step almost collocation methods for ordinary differential equations
• Continuous two-step Runge-Kutta methods for ordinary differential equations
• A PI stepsize control for the numerical solution of ordinary differential equations
• Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
• Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
• Automatic control and adaptive time-stepping
• Two-step almost collocation methods for Volterra integral equations
• The Order of Numerical Methods for Ordinary Differential Equations
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• Digital filters in adaptive time-stepping