Stability of Parabolic Difference Approximations to Certain Mixed Initial Boundary Value Problems
- 1 January 1972
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 26 (117) , 13-39
- https://doi.org/10.2307/2004715
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.
Keywords
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