On the roles of ``stability'' and ``convergence'' in semidiscrete projection methods for initial-value problems

Author:
Seymour V. Parter

Journal:
Math. Comp. **34** (1980), 127-154

MSC:
Primary 65N35; Secondary 34G99

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551294-9

MathSciNet review:
551294

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the initial value problem (1.1)

*A*is a linear operator taking into

*X*, where

*X*is a Banach space. Consider also semidiscrete numerical methods of the form: find such that

The study of such numerical methods may be related to the approximation of semigroups and Laplace transform methods making use of the resolvent operators . The basic results require stability or weak stability and give convergence rates of the same order as in the steady state problems.

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0551294-9

Article copyright:
© Copyright 1980
American Mathematical Society