Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
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.

References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M05

Retrieve articles in all journals with MSC: 65M05

Additional Information

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

American Mathematical Society