A finite-difference method for parabolic differential equations with mixed derivatives
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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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