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Mathematics of Computation

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



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
MathSciNet review: 0298990
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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