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Transfer of boundary conditions for difference equations. (English) Zbl 1003.65118

This paper deals with the transferring boundary conditions for solving a linear difference equation of the second order. The author shows that the boundary conditions can be transferred to any point similarly as in the continuous case. Moreover, it is found out that some results of this kind may be obtained also for some particular two-dimensional problems. As an example of the application of the idea of transferring boundary conditions in the two-dimensional case, the author deals with a discrete analogue of the Dirichlet problem for the Laplace equation on a rectangle.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65F50 Computational methods for sparse matrices
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
39A10 Additive difference equations
65Q05 Numerical methods for functional equations (MSC2000)
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References:

[1] J. Taufer: Lösung der Randwertprobleme von linearen Differentialgleichungen. Rozpravy ČSAV, Řada mat. a přír. věd, Vol. 83. Academia, Praha, 1973.
[2] G. H. Meyer: Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding. Academic Press, New York, 1973. · Zbl 0304.34018
[3] E. Vitásek: Approximate solution of ordinary differential equations. Survey of Applicable Mathematics (K. Rektorys and E. Vitásek, Kluwer Academic Publishers, Dordrecht, 1994, pp. 478-533.
[4] E. Vitásek: Remark to the problem of transferring boundary conditions in two dimensions. Proceedings of the Prague Mathematical Conference 1996, Icaris, Praha, 1997, pp. 337-342. · Zbl 0963.65528
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