Backward Error Analysis for Numerical Integrators
Please always quote using this URN: urn:nbn:de:0297-zib-2320
- We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable step-size integration of Hamiltonian systems, the conservation of adiabatic invariants, and numerical chaos associated to homoclinic orbits.
Author: | Sebastian Reich |
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Document Type: | ZIB-Report |
Date of first Publication: | 1996/07/16 |
Series (Serial Number): | ZIB-Report (SC-96-21) |
ZIB-Reportnumber: | SC-96-21 |
Published in: | Appeared in: SIAM J. Numer. Anal. 36 (1999) 1549-1579 |