L. F. Spevak, O. A. Nefedova

A NUMERICAL SOLUTION TO A SYSTEM OF TWO COUPLED ELLIPTIC EQUATIONS

A solution is constructed for a system of two coupled elliptic equations. An iterative numerical algorithm based on the method of partial solutions, the collocation method, and the boundary element method is proposed for a boundary value problem in a specified two-dimensional region. The algorithm is implemented as a program with the use of the OpenMP open standard of concurrent programming. To verify the algorithm and the program, simple exact solutions are found for two particular cases of the system under study. A computational experiment is performed, showing a good agreement of the calculation results with the exact solutions. Computer-assisted convergence of the numerical algorithm with respect to the number of boundary element nodes and collocation points is demonstrated.

Acknowledgment: The work was performed under the state assignment, registration number 124020600042-9.

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