Article
MSC:
35J05,
39A10,
65F50,
65N06,
65N22,
65Q05 | MR 1800965 | Zbl 1003.65118 | DOI: 10.1023/A:1022385517615
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Keywords:
difference equation; sparse matrices; boundary value problems
difference equation; sparse matrices; boundary value problems
Summary:
It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.
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. MR 0488791 | Zbl 0304.34018
[3] E. Vitásek: Approximate solution of ordinary differential equations. In: Survey of Applicable Mathematics (K. Rektorys and E. Vitásek, eds.), Kluwer Academic Publishers, Dordrecht, 1994, pp. 478–533.
[4] E. Vitásek: Remark to the problem of transferring boundary conditions in two dimensions. In: Proceedings of the Prague Mathematical Conference 1996, Icaris, Praha, 1997, pp. 337–342. MR 1703984
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