A finite-difference method for parabolic differential equations with mixed derivatives
Author:
Jan Krzysztof Kowalski
Journal:
Math. Comp. 25 (1971), 675-698
MSC:
Primary 65M05
DOI:
https://doi.org/10.1090/S0025-5718-1971-0309322-6
MathSciNet review:
0309322
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Abstract | References | Similar Articles | Additional Information
Abstract: In a recent paper, P. Jamet constructed a positive difference operator for a parabolic differential operator whose coefficients are singular on the boundary, and proved the existence of a unique solution of the boundary-value problem for the differential equation using discrete barriers. In the present paper, Jamet's results are extended to the parabolic operator with mixed derivatives.
- [1] R. Courant, K. Friedrichs, and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928), no. 1, 32–74 (German). MR 1512478, https://doi.org/10.1007/BF01448839
- [2] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
- [3] Pierre Jamet, Numerical methods and existence theorems for parabolic differential equations whose coefficients are singular on the boundary, Math. Comp. 22 (1968), 721–743. MR 0255084, https://doi.org/10.1090/S0025-5718-1968-0255084-0
- [4] Fritz John, Lectures on advanced numerical analysis, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0221721
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1971-0309322-6
Keywords:
Parabolic differential operator,
boundary-value problem,
mixed derivatives,
positive difference operator,
consistency of operators,
convergence on the mesh,
discrete barrier
Article copyright:
© Copyright 1971
American Mathematical Society
