Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability

DOI10.1016/j.apnum.2018.10.001zbMath1405.65086OpenAlexW2897402918WikidataQ129108686 ScholiaQ129108686MaRDI QIDQ1633319

Zdzisław Jackiewicz, Ali Abdi

Publication date: 19 December 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.10.001

zbMATH Keywords

general linear methodsNordsieck representationinherent Runge-Kutta stabilityadaptive stepsize and order selection

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)

Related Items (15)

Generalized second derivative linear multistep methods for ordinary differential equations ⋮ EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ⋮ An adaptive one-point second-derivative Lobatto-type hybrid method for solving efficiently differential systems ⋮ Recent advances in the numerical solution of Volterra integral equations ⋮ On the implementation of explicit two-step peer methods with Runge-Kutta stability ⋮ Implementation of second derivative general linear methods ⋮ Implicit-explicit second derivative diagonally implicit multistage integration methods ⋮ A new one-step method with three intermediate points in a variable step-size mode for stiff differential systems ⋮ Implementation of general linear methods for Volterra integral equations ⋮ A GLMs-based difference-quadrature scheme for Volterra integro-differential equations ⋮ Projection of second derivative methods for ordinary differential equations with invariants ⋮ Variable stepsize SDIMSIMs for ordinary differential equations ⋮ Unnamed Item ⋮ A new code for Volterra integral equations based on natural Runge-Kutta methods ⋮ Multivalue second derivative collocation methods

Uses Software

• Matlab
• DIMSIM
• bvp4c
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

• Unnamed Item
• Unnamed Item
• A PI stepsize control for the numerical solution of ordinary differential equations
• A new approach to error estimation for general linear methods
• The construction of practical general linear methods
• Implementation of DIMSIMs for stiff differential systems
• Unconditionally stable general linear methods for ordinary differential equations
• Construction of general linear methods with Runge-Kutta stability properties
• Automatic control and adaptive time-stepping
• Explicit general linear methods with inherent Runge--Kutta stability
• Experiments with a variable-order type 1 DIMSIM code
• Error propagation of general linear methods for ordinary differential equations
• The MATLAB ODE Suite
• Solving Ordinary Differential Equations I
• Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
• Solving ODEs with MATLAB
• Comparing Numerical Methods for Ordinary Differential Equations

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