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
Full-text PDF
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 & H. Lewy, ``Über die Differenzengleichungen der mathematischen Physik,'' Math. Ann., v. 100, 1928, pp. 32-74; English transl., IBM J., v. 11, 1967, pp. 215-234. MR 1512478
- [2] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964; Russian transl., ``Mir,'' Moscow, 1968. MR 31 #6062. MR 0181836 (31:6062)
- [3] P. Jamet, ``Numerical methods and existence theorems for parabolic differential equations whose coefficients are singular on the boundary,'' Math. Comp., v. 22, 1968, pp. 721-743. MR 40 #8291. MR 0255084 (40:8291)
- [4] F. John, Lectures on Advanced Numerical Analysis, Gordon and Breach, New York, 1967. MR 36 #4773. MR 0221721 (36:4773)
Retrieve articles in Mathematics of Computation with MSC: 65M05
Retrieve articles in all journals with MSC: 65M05
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