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Mathematics of Computation

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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
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.


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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