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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

The modified Newton method in the solution of stiff ordinary differential equations


Author: Roger Alexander
Journal: Math. Comp. 57 (1991), 673-701
MSC: Primary 65L05; Secondary 34A50, 34A65, 65H10
MathSciNet review: 1094939
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Abstract: This paper presents an analysis of the modified Newton method as it is used in codes implementing implicit formulae for integrating stiff ordinary differential equations. We prove that near a smooth solution of the differential system, when the Jacobian is essentially negative dominant and slowly varying, the modified Newton iteration is contractive, converging to the locally unique solution--whose existence is hereby demonstrated--of the implicit equations. This analysis eliminates several common restrictive or unrealistic assumptions, and provides insight for the design of robust codes.


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DOI: https://doi.org/10.1090/S0025-5718-1991-1094939-7
Keywords: Stiff differential equations, modified Newton method
Article copyright: © Copyright 1991 American Mathematical Society