A survey of shadowing methods for numerical solutions of ordinary differential equations

Authors:
Wayne Hayes;Kenneth R. Jackson
Affiliations:
Computer Science Department, University of Toronto, Toronto, Ontario, Canada;Computer Science Department, University of Toronto, Toronto, Ontario, Canada
Venue:
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Year:
2005

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Abstract

A shadow is an exact solution to a set of equations that remains close to a numerical solution for a long time. Shadowing can thus be used as a form of backward error analysis for numerical solutions to ordinary differential equations. This survey introduces the reader to shadowing with a detailed tour of shadowing algorithms and practical results obtained over the last 15 years.