Analysis of variable-stepsize linear multistep methods with special emphasis on symmetric ones
DOI10.1090/S0025-5718-03-01538-2zbMath1029.65081OpenAlexW1979507655MaRDI QIDQ4417159
Publication date: 28 July 2003
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01538-2
stabilitynumerical resultsperiodic orbitsreversible systemslinear multistep methodserror growthasymptotic expansion of the errorvariable stepsizessymmetric integrators
Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Stability and convergence of numerical methods for ordinary differential equations (65L20) Two-body problems (70F05) 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) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)
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Cites Work
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- Variable step implementation of geometric integrators
- Variable time step integration with symplectic methods
- Variable steps for reversible integration methods
- Accurate long-term integration of dynamical systems
- A generalization to variable stepsizes of Störmer methods for second-order differential equations
- The Adaptive Verlet Method
- Reversible Long-Term Integration with Variable Stepsizes
- Solving Ordinary Differential Equations I
- The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
- The Effect of Variable Mesh Size on the Stability of Multistep Methods
- Backward Error Analysis for Numerical Integrators
- Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems
- Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems
- A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems