Linear conservation laws for ODEs

DOI10.1016/S0898-1221(98)00071-6zbMath0999.65071OpenAlexW1963968964MaRDI QIDQ1608399

Lawrence F. Shampine

Publication date: 6 August 2002

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(98)00071-6

zbMATH Keywords

algorithmsconservation lawsdifferential-algebraic equationsmethod of linesNavier-Stokes equationRunge-Kutta methodslinear multistep methodsAdams method

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Nonlinear ordinary differential equations and systems (34A34) Navier-Stokes equations (35Q30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for differential-algebraic equations (65L80)

Related Items (5)

The regularization continuation method with an adaptive time step control for linearly constrained optimization problems ⋮ A comprehensive theory on generalized BBKS schemes ⋮ Conservation laws and the numerical solution of ODEs. II ⋮ A second-order pseudo-transient method for steady-state problems ⋮ Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations

Uses Software

• Matlab
• VODE
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

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• Conservation properties of numerical integration methods for systems of ordinary differential equations
• The MATLAB ODE Suite
• VODE: A Variable-Coefficient ODE Solver
• ODE solvers and the method of lines
• Maintaining Solution Invariants in the Numerical Solution of ODE<scp>s</scp>
• A modified finite element method for solving the time‐dependent, incompressible Navier‐Stokes equations. Part 1: Theory
• A note on the numerical integration of conservative systems of first-order ordinary differential equations
• The automatic integration of ordinary differential equations
• Comparing Numerical Methods for Ordinary Differential Equations

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