The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Existence of Non-spurious Solutions to Discrete Boundary Value Problems


Irena Rachunkova and Christopher C. Tisdell

Department of Mathematics
Palacky University
771 46 Olomouc, Czech Republic.

School of Mathematics
The University of New South Wales
Sydney 2052, Australia.


This paper investigates discrete boundary value problems (BVPs) involving second-order difference equations and two-point boundary conditions. General theorems guaranteeing the existence and uniqueness of solutions to the discrete BVP are established. The methods involve a sufficient growth condition to yield an a priori bound on solutions to a certain family of discrete BVPs. The em a priori bounds on solutions to the discrete BVP do not depend on the step-size and thus there are no ``spurious'' solutions. It is shown that solutions of the discrete BVP will converge to solutions of ordinary differential equations.

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