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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 3, 1993, pp. 549–566
DOI: 10.4171/ZAA/548

Published online: 1993-09-30

Exact Difference Schemes and Difference Schemes of Arbitrary Given Degree of Accuracy for Generalized One-Dimensional Third Boundary Value Problems

I.P. Gavrilyuk[1]

(1) Universität Leipzig, Germany

A variational problem is formulated which is a generalization of the third boundary value problem for one-dimensional equations. Conditions of existence and uniqueness of solutions are considered. The numerical approximation of arbitrary given degree of accuracy (truncated difference schemes) regarded in this paper is based on the three-point difference relations for the exact solution (exact difference scheme).

Keywords: Exact and truncated three-point difference schemes, generalized Cauchy problems, stability of coefficients

Gavrilyuk I.P.: Exact Difference Schemes and Difference Schemes of Arbitrary Given Degree of Accuracy for Generalized One-Dimensional Third Boundary Value Problems. Z. Anal. Anwend. 12 (1993), 549-566. doi: 10.4171/ZAA/548