Maximum norm stability of difference approximations to the mixed initial boundary-value problem for the heat equation

Author:
J. M. Varah

Journal:
Math. Comp. **24** (1970), 31-44

MSC:
Primary 65.68

DOI:
https://doi.org/10.1090/S0025-5718-1970-0260215-1

MathSciNet review:
0260215

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Abstract: We consider the heat equation in the quarter-plane , with initial condition and boundary condition . We are concerned with the stability of difference approximations to this problem. Using the resolvent operator , we give sufficient conditions for consistent, onestep explicit schemes to be stable in the maximum norm.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0260215-1

Keywords:
Stability,
difference methods,
mixed initial boundary-value problem,
heat equation

Article copyright:
© Copyright 1970
American Mathematical Society