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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: 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?)

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  • [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)

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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

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