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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

$\displaystyle {u_t} - a(x,t){u_{xx}} - b(x,t){u_x} - c(x,t)u = f(x,t)$

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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0298990-4
Keywords: Stability, difference methods, parabolic, initial boundary value problem
Article copyright: © Copyright 1972 American Mathematical Society

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