Mesh refinements for parabolic equations of second order

Author:
Stewart Venit

Journal:
Math. Comp. **27** (1973), 745-754

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1973-0381337-3

MathSciNet review:
0381337

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Abstract | References | Similar Articles | Additional Information

Abstract: Given certain implicit difference approximations to in the region , with a finer *x*-mesh width in the left half-plane than in the right, we consider the stability in the maximum norm of these schemes using several different interface conditions (at ). In order to obtain our results, we first prove a stability theorem for certain simple second-order parabolic initial boundary systems on an evenly spaced mesh in the right half-plane alone. By a standard procedure, the first problem is converted into the second one, and solved in this manner.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0381337-3

Keywords:
Difference scheme,
stability,
mesh refinement,
parabolic partial differential equation,
initial boundary-value problem

Article copyright:
© Copyright 1973
American Mathematical Society