Abstract
We are interested in studying the stable difference schemes for the numerical solution of the nonlocal boundary value problem with the Dirichlet‐Neumann condition for the multidimensional elliptic equation. The first and second orders of accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two‐dimensional elliptic differential equation. The method is illustrated by numerical examples.
Highlights
Methods of solution of the Bitsadze-Samarskii nonlocal boundary value problems for elliptic differential equations have been studied extensively by many researchers see 1–22 and the references given therein
Applying difference scheme 2.5, we present the first order of accuracy difference scheme for the approximate solution of problem 3.1 is 1 − 2ukn τ2 ukn−1
The theoretical statements for the solution of these difference schemes are supported by the results of numerical examples
Summary
Methods of solution of the Bitsadze-Samarskii nonlocal boundary value problems for elliptic differential equations have been studied extensively by many researchers see 1–22 and the references given therein. Xm : 0 < xk < 1, 1 ≤ k ≤ m with boundary S, Ω Ω ∪ S. In 0, 1 × Ω, the Bitsadze-Samarskii-type nonlocal boundary value problem for the multidimensional elliptic equation m. We are interested in studying the stable difference schemes for the numerical solution of the nonlocal boundary value problem 1. The first and second orders of accuracy difference schemes are presented. The stability and almost coercive stability of these difference schemes are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of two-dimensional elliptic partial differential equations
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