Stability of parabolic difference approximations to certain mixed initial boundary value problems

Author:
Stanley Osher

Journal:
Math. Comp. **26** (1972), 13-39

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1972-0298990-4

MathSciNet review:
0298990

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the equation \[ {u_t} - a(x,t){u_{xx}} - b(x,t){u_x} - c(x,t)u = f(x,t)\] in a region $0 \leqq x \leqq 1,t \geqq 0$, with inhomogeneous initial and boundary data. We are concerned with stability and estimates on divided differences in the maximum norm for solutions of consistent implicit, multistep, parabolic difference approximations to this problem. Using a parametrix approach, we give sufficient conditions for certain estimates to be valid.

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Keywords:
Stability,
difference methods,
parabolic,
initial boundary value problem

Article copyright:
© Copyright 1972
American Mathematical Society