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Banei, Siamak, Shanazari, Kamal. (1400). Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method. سامانه مدیریت نشریات علمی, 9(4), 1083-1099. doi: 10.22034/cmde.2020.35767.1627
Siamak Banei; Kamal Shanazari. "Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method". سامانه مدیریت نشریات علمی, 9, 4, 1400, 1083-1099. doi: 10.22034/cmde.2020.35767.1627
Banei, Siamak, Shanazari, Kamal. (1400). 'Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method', سامانه مدیریت نشریات علمی, 9(4), pp. 1083-1099. doi: 10.22034/cmde.2020.35767.1627
Banei, Siamak, Shanazari, Kamal. Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method. سامانه مدیریت نشریات علمی, 1400; 9(4): 1083-1099. doi: 10.22034/cmde.2020.35767.1627

Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method

Computational Methods for Differential Equations
مقاله 11، دوره 9، شماره 4، دی 2021، صفحه 1083-1099    اصل مقاله (565.17 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.35767.1627
نویسندگان
Siamak Banei؛ Kamal Shanazari*
Department of mathematics, University of Kurdistan, Sanandaj, Iran.
چکیده
‎‎‎‎‎In this paper, we present a numerical technique to deal with the one-dimensional forward-backward heat equations. First, the physical domain is divided into two non-overlapping subdomains resulting in two separate forward and backward subproblems, and then a meshless method based on multiquadric radial basis functions is employed to treat the spatial variables in each subproblem using the Kansa’s method. We use a time discretization scheme to approximate the time derivative by the forward and backward finite difference formulas. In order to have adequate boundary conditions for each subproblem, an initial approximate solution is assumed on the interface boundary, and the solution is improved by solving the subproblems in an iterative way. The numerical results show that the proposed method is very useful and computationally efficient in comparison with the previous works.
کلیدواژه‌ها
Forward-backward heat equation؛ Non-overlapping domain decomposition؛ Radial basis functions؛ Meshless methods
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