A posteriori bounds in the numerical solution of mildly nonlinear parabolic equations

Author:
Alfred Carasso

Journal:
Math. Comp. **24** (1970), 785-792

MSC:
Primary 65.68

DOI:
https://doi.org/10.1090/S0025-5718-1970-0281374-0

MathSciNet review:
0281374

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Abstract: We derive a posteriori bounds for and its difference quotient , where and are, respectively, the exact and computed solution of a difference approximation to a mildly nonlinear parabolic initial boundary problem, with a known steadystate solution. It is assumed that the computation is over a long interval of time. The estimates are valid for a class of difference approximations, which includes the CrankNicolson method, and are of the same magnitude for both and .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0281374-0

Keywords:
Parabolic equations,
Crank-Nicolson method,
limiting steady state,
computations over long times

Article copyright:
© Copyright 1970
American Mathematical Society