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On global error estimation and control for initial value problems
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DOI：10.1137/050646950.png)
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Abstract
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This paper addresses global error estimation and control for initial value problems for ordinary differential equations. The focus lies on a comparison between a novel approach based on the adjoint method combined with a small sample statistical initialization and the classical approach based on the first variational equation. Control is achieved through tolerance proportionality. Both approaches are found to work well and to enable estimation and control in a reliable manner.
Keywords:
numerical integration for ODEs
global error estimation
global error control
defects and local errors
tolerance proportionality
adjoint method
small sample statistical initialization
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