Abstract
Alternating direction implicit (A.D.I.) methods are proposed for solving the parabolic equation with variable coefficients in two and three space dimensions with mixed derivatives. The methods require the solution of two tridiagonal sets of equations at each time step in the two space dimensional case, and three tridiagonal sets of equations in the three space dimensional case. Several theorems are stated showing the methods to be unconditionally stable for certain ranges of an auxiliary parameter. Reference is made to other authors and numerical results are mentioned.
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McKee, S. (1969). Alternating direction methods for parabolic equations in two and three space dimensions with mixed derivatives. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060029
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DOI: https://doi.org/10.1007/BFb0060029
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