Rahimi, Asghar, Shivanian, Elyas. (1403). An efficient RBF-FD method using polyharmonic splines alongside polynomials for the numerical solution of two-dimensional PDEs held on irregular domains and subject to Dirichlet and Robin boundary conditions. هنرهای کاربردی, 15(4), 173-184. doi: 10.22075/ijnaa.2023.28181.3826
Asghar Rahimi; Elyas Shivanian. "An efficient RBF-FD method using polyharmonic splines alongside polynomials for the numerical solution of two-dimensional PDEs held on irregular domains and subject to Dirichlet and Robin boundary conditions". هنرهای کاربردی, 15, 4, 1403, 173-184. doi: 10.22075/ijnaa.2023.28181.3826
Rahimi, Asghar, Shivanian, Elyas. (1403). 'An efficient RBF-FD method using polyharmonic splines alongside polynomials for the numerical solution of two-dimensional PDEs held on irregular domains and subject to Dirichlet and Robin boundary conditions', هنرهای کاربردی, 15(4), pp. 173-184. doi: 10.22075/ijnaa.2023.28181.3826
Rahimi, Asghar, Shivanian, Elyas. An efficient RBF-FD method using polyharmonic splines alongside polynomials for the numerical solution of two-dimensional PDEs held on irregular domains and subject to Dirichlet and Robin boundary conditions. هنرهای کاربردی, 1403; 15(4): 173-184. doi: 10.22075/ijnaa.2023.28181.3826

An efficient RBF-FD method using polyharmonic splines alongside polynomials for the numerical solution of two-dimensional PDEs held on irregular domains and subject to Dirichlet and Robin boundary conditions

International Journal of Nonlinear Analysis and Applications
مقاله 15، دوره 15، شماره 4، تیر 2024، صفحه 173-184    اصل مقاله (788.32 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28181.3826
نویسندگان
Asghar Rahimi1؛ Elyas Shivanian* 2
1Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran
2Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran
چکیده
In the present paper, the relatively new method of Radial Basis Function-Generated Finite Difference (RBF-FD) is used to solve a class of Partial Differential Equations (PDEs) with Dirichlet and Robin boundary conditions. For this approximation, Polyharmonic Splines (PHS) are used alongside Polynomials. This combination has many benefits. On the other hand, Polyharmonic Splines have no shape parameter and therefore relieve us of the hassle of calculating the optimal shape parameter. As the first problem, a two-dimensional Poisson equation with the Dirichlet boundary condition is investigated in various domains. Then, an elliptic PDE with the Robin boundary condition is solved by the proposed method. The results of numerical studies indicate the excellent efficiency, accuracy and high speed of the method, while for these studies, very fluctuating and special test functions have been used.
کلیدواژه‌ها
Partial Differential Equations؛ Radial basis functions؛ Polyharmonic Splines؛ Robin boundary condition؛ RBF-FD
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