Differential and difference variants of 2-d nonlocal boundary value problem with poisson’s operator
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Date
2019
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Publisher
Maltepe Üniversitesi
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CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Abstract
Applying [1] and [2] in rectangular ? = (0 < x < 1) × (0 < y < ?) in differential and difference variants of two-dimensional nonlocal boundary value problems with Poisson’s operator are investigated. Theorem 1. Let f(x, y) ? C 0 (?), then classical solution of the differential problem exists and a priori estimate holds
u(x, y)
W2 2 (?) ? C1
f(x, y)
L2(?). Theorem 2. Let u(x, y) ? C (4)(?) for the solution of the differential problem, then solution Y of difference problem approximates classical solution u(x, y) with second order of accuracy in h = (h 2 1 + h 2 2 ) 1/2 when h2 ? 0 .
u(x, y)
W2 2 (?) ? C1
f(x, y)
L2(?). Theorem 2. Let u(x, y) ? C (4)(?) for the solution of the differential problem, then solution Y of difference problem approximates classical solution u(x, y) with second order of accuracy in h = (h 2 1 + h 2 2 ) 1/2 when h2 ? 0 .
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Keywords
Poisson’s operator, Nonlocal boundary, Difference problem
Journal or Series
International Conference of Mathematical Sciences (ICMS 2019)
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Citation
Dovletov, D. M. (2019). Differential and difference variants of 2-d nonlocal boundary value problem with poisson’s operator. International Conference of Mathematical Sciences (ICMS 2019). s. 129.
