Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M15, 65N30

Retrieve articles in all journals with MSC: 65M15, 65N30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0537961-3
PII: S 0025-5718(1979)0537961-3
Keywords: Cauchy problem, error estimates, improperly posed problem
Article copyright: © Copyright 1979 American Mathematical Society