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Numerical approximation of a Cauchy problem for a parabolic partial differential equation


Authors: Richard E. Ewing and Richard S. Falk
Journal: Math. Comp. 33 (1979), 1125-1144
MSC: Primary 65M15; Secondary 65N30
MathSciNet review: 537961
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Abstract: A procedure for the numerical approximation of the Cauchy problem for the following linear parabolic partial differential equation is defined:

\begin{displaymath}\begin{array}{*{20}{c}} {{u_t} - {{(p(x){u_x})}_x} + q(x)u = ... ... \leqslant 1,0 \leqslant t \leqslant T.} \hfill \\ \end{array} \end{displaymath}

The procedure involves Galerkin-type numerical methods for related parabolic initial boundary-value problems and a linear programming problem. Explicit a priori error estimates are presented for the entire discrete procedure when the data $ {f_1}$, $ {f_2}$, and g are known only approximately.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0537961-3
Keywords: Cauchy problem, error estimates, improperly posed problem
Article copyright: © Copyright 1979 American Mathematical Society