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

Osher, Stanley

doi:10.1090/S0025-5718-1972-0298990-4

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: 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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