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Reihani, Parastoo, Esmailpour, Hossein, Soltanian, Fahimeh. (1401). An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions. سامانه مدیریت نشریات علمی, 11(1), 143-160. doi: 10.22034/cmde.2022.49491.2060
Parastoo Reihani; Hossein Esmailpour; Fahimeh Soltanian. "An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions". سامانه مدیریت نشریات علمی, 11, 1, 1401, 143-160. doi: 10.22034/cmde.2022.49491.2060
Reihani, Parastoo, Esmailpour, Hossein, Soltanian, Fahimeh. (1401). 'An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions', سامانه مدیریت نشریات علمی, 11(1), pp. 143-160. doi: 10.22034/cmde.2022.49491.2060
Reihani, Parastoo, Esmailpour, Hossein, Soltanian, Fahimeh. An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions. سامانه مدیریت نشریات علمی, 1401; 11(1): 143-160. doi: 10.22034/cmde.2022.49491.2060

An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions

Computational Methods for Differential Equations
مقاله 11، دوره 11، شماره 1، فروردین 2023، صفحه 143-160    اصل مقاله (819.19 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.49491.2060
نویسندگان
Parastoo Reihani* ؛ Hossein Esmailpour؛ Fahimeh Soltanian
Department of Mathematics, Payame Noor University (PNU), P. O. Box: 19395-4697, Tehran, Iran.
چکیده
In the present study, we consider an important mathematical model of the spread of two competing species in an ecological system with two species considering the interactions between these species. This model is derived from a system of nonlinear reaction-diffusion equations. We investigate this model as an inverse problem. Using appropriate initial and boundary conditions, the finite difference method in the time variable and the Quartic Bspline collocation method in the spatial variable are used to develop a numerical method. The proposed numerical approach results in an ill-posed linear system of equations and to overcome the ill-posedness, the Tikhonov regularization method is implemented. An effective approach based on the ABC algorithm is established to determine the regularization parameter. To show the robustness and ability of the present approach, for a test case, the results are compared with the results of the L-curve and GCV methods.
کلیدواژه‌ها
Inverse problem؛ Reaction-Diffusion problem؛ Regularization؛ ABS algorithm
مراجع
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