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Title: Difference equations in banach spaces
Authors: Agarwal, R.P. 
Thompson, H.B.
Tisdell, C.C.
Keywords: A priori bounds
Difference equations
Existence of solutions
Second-order ordinary differential equations
Two point boundary value problem
Issue Date: Mar-2003
Citation: Agarwal, R.P., Thompson, H.B., Tisdell, C.C. (2003-03). Difference equations in banach spaces. Computers and Mathematics with Applications 45 (6-9) : 1437-1444. ScholarBank@NUS Repository.
Abstract: Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented.
Source Title: Computers and Mathematics with Applications
ISSN: 08981221
DOI: 10.1016/S0898-1221(03)00100-7
Appears in Collections:Staff Publications

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