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Mathematics of Computation

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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
MathSciNet review: 0281374
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Abstract: We derive a posteriori bounds for $ (V - \hat V)$ and its difference quotient $ {(V - \hat V)_x}$, where $ V$ and $ \hat V$ 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 $ (V - \hat V)$ and $ (V - \hat V)x$.

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Keywords: Parabolic equations, Crank-Nicolson method, limiting steady state, computations over long times
Article copyright: © Copyright 1970 American Mathematical Society

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