On the convergence of difference approximations to nonlinear contraction semigroups in Hilbert spaces

Author:
Olavi Nevanlinna

Journal:
Math. Comp. **32** (1978), 321-334

MSC:
Primary 47H15; Secondary 65J05

DOI:
https://doi.org/10.1090/S0025-5718-1978-0513203-9

MathSciNet review:
0513203

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Abstract | References | Similar Articles | Additional Information

Abstract: Convergence properties of the difference schemes (S)

*A*is a nonlinear, maximally monotone operator in a real Hilbert space. It is shown, in particular, that if the scheme (S) is consistent and stable for the test equation for , where

*K*is a compact subset of the right half-plane, then (S) is convergent as , with suitable initial values, for (E), on compact intervals [0,

*T*]. Moreover, the convergence is uniform on the half-axis , if the solution tends strongly to a constant as . We also show that under weaker stability conditions one can construct conditionally convergent methods.

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0513203-9

Article copyright:
© Copyright 1978
American Mathematical Society