P C Moan 2006 J. Phys. A: Math. Gen. 39 5545 doi:10.1088/0305-4470/39/19/S13
On modified equations for discretizations of ODEs
P C Moan
Show affiliationsThe theory of modified equations (MEs) for discretizations of ODEs is reconsidered. Obstructions to convergence of series expansions of MEs are pinpointed and alternative approaches are presented which provide more accurate descriptions of numerical approximations through MEs. We emphasize how structural assumptions on the ODE can be used to improve estimates. Then we give arguments for a slightly alternative approach based on time-dependent MEs which avoids the asymptotic nature traditionally associated with MEs. Some applications of the theory are also provided.
- PACS
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02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
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65L20 Stability and convergence of numerical methods
37C55 Periodic and quasiperiodic flows and diffeomorphisms
37C10 Vector fields, flows, ordinary differential equations
40A05 Convergence and divergence of series and sequences
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
- Subjects
- Dates
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Issue 19 (12 May 2006)
Received 2 September 2005, in final form 2 February 2006
Published 24 April 2006
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On modified equations for discretizations of ODEs
P C Moan 2006 J. Phys. A: Math. Gen. 39 5545
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