2021, Vol. 2, Issue 1, Part A
Numerical solution of non-linear non-local problems for elliptic equations
Author(s): Dilshod Barakaev
Abstract: A non-local problem for an elliptic equation in a rectangular domain was investigated. A rectangular grid for the corresponding difference problem was constructed and the error of the approximate solutions of non-local problems was estimated. Various application problems (heat conductivity [1, 2, 3], fluid mechanics [4], the theory of elasticity and shells [5], etc.) are reduced to non-local boundary value problems. Non-local boundary conditions are especially difficult for justiï¬cation of classical ï¬nite difference schemes due to the complexity of the structure of the matrices obtained from systems of equations. This difficulty manifests itself especially in the justiï¬cation of numerical methods in the case of non-linear equations. In this paper we consider the non-local boundary value problem for a quasi-linear equation. We found the numerical solutions of stated problem using the ï¬nite difference method, and estimated the error of the approximate solutions of non-local problems.
Pages: 01-12 | Views: 895 | Downloads: 397
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How to cite this article:
Dilshod Barakaev. Numerical solution of non-linear non-local problems for elliptic equations. Journal of Mathematical Problems, Equations and Statistics. 2021; 2(1): 01-12.
