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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Mesh refinements for parabolic equations of second order

Author: Stewart Venit
Journal: Math. Comp. 27 (1973), 745-754
MSC: Primary 65M10
MathSciNet review: 0381337
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Abstract: Given certain implicit difference approximations to $ {u_t} = a(x){u_{xx}} + b(x){u_x} + c(x)u$ in the region $ - \infty < x < \infty ,t \geqq 0$, 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 $ x = 0$). 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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Keywords: Difference scheme, stability, mesh refinement, parabolic partial differential equation, initial boundary-value problem
Article copyright: © Copyright 1973 American Mathematical Society