Some locally one-dimensional difference schemes for parabolic equations in an arbitrary region

Some locally one-dimensional difference schemes for parabolic equations in an arbitrary region
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by Bert Hubbard PDF

Math. Comp. 20 (1966), 53-59 Request permission

References

J. H. Bramble and B. E. Hubbard, On the formulation of finite difference analogues of the Dirichlet problem for Poisson’s equation, Numer. Math. 4 (1962), 313–327. MR 149672, DOI 10.1007/BF01386325
Jim Douglas Jr., On the numerical integration of $\partial ^2u/\partial x^2+\partial ^2u/\partial y^2=\partial u/\partial t$ by implicit methods, J. Soc. Indust. Appl. Math. 3 (1955), 42–65. MR 71875
Bert E. Hubbard, Alternating direction schemes for the heat equation in a general domain, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 448–463. MR 196952
D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math. 3 (1955), 28–41. MR 71874
A. A. Samarskiĭ, An efficient difference method for solving a multidimensional parabolic equation in an arbitrary domain, Ž. Vyčisl. Mat i Mat. Fiz. 2 (1962), 787–811 (Russian). MR 183127