Conservation laws and the numerical solution of ODEs. II

DOI10.1016/S0898-1221(99)00183-2zbMath0947.65086OpenAlexW1988018377MaRDI QIDQ1963080

Lawrence F. Shampine

Publication date: 20 January 2000

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

Full work available at URL: https://doi.org/10.1016/s0898-1221(99)00183-2

zbMATH Keywords

numerical experimentserror boundstiff problemsvariable stepsizecoordinate projection methodside conditionsRunge-Kutta algorithmsmultistep difference approximations

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (6)

The regularization continuation method with an adaptive time step control for linearly constrained optimization problems ⋮ Numerical solution of differential-algebraic equations for constrained mechanical motion ⋮ General relaxation methods for initial-value problems with application to multistep schemes ⋮ A second-order pseudo-transient method for steady-state problems ⋮ Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations ⋮ Nonnegative solutions of ODEs

Uses Software

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

Cites Work

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• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Stabilization of DAEs and invariant manifolds
• Linear conservation laws for ODEs
• Stabilization of constraints and integrals of motion in dynamical systems
• The MATLAB ODE Suite
• Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints
• ODE solvers and the method of lines
• Maintaining Solution Invariants in the Numerical Solution of ODE<scp>s</scp>
• The automatic integration of ordinary differential equations

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