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Ghaznavi, Mehrdad, Noori Skandari, Mohammad Hadi. (1403). A Chebyshev pseudo-spectral based approach for solving Troesch’s problem with convergence analysis. سامانه مدیریت نشریات علمی, 12(4), 827-841. doi: 10.22034/cmde.2024.56313.2355
Mehrdad Ghaznavi; Mohammad Hadi Noori Skandari. "A Chebyshev pseudo-spectral based approach for solving Troesch’s problem with convergence analysis". سامانه مدیریت نشریات علمی, 12, 4, 1403, 827-841. doi: 10.22034/cmde.2024.56313.2355
Ghaznavi, Mehrdad, Noori Skandari, Mohammad Hadi. (1403). 'A Chebyshev pseudo-spectral based approach for solving Troesch’s problem with convergence analysis', سامانه مدیریت نشریات علمی, 12(4), pp. 827-841. doi: 10.22034/cmde.2024.56313.2355
Ghaznavi, Mehrdad, Noori Skandari, Mohammad Hadi. A Chebyshev pseudo-spectral based approach for solving Troesch’s problem with convergence analysis. سامانه مدیریت نشریات علمی, 1403; 12(4): 827-841. doi: 10.22034/cmde.2024.56313.2355

A Chebyshev pseudo-spectral based approach for solving Troesch’s problem with convergence analysis

Computational Methods for Differential Equations
مقاله 14، دوره 12، شماره 4، دی 2024، صفحه 827-841    اصل مقاله (508.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.56313.2355
نویسندگان
Mehrdad Ghaznavi* ؛ Mohammad Hadi Noori Skandari
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
چکیده
In this article, the Chebyshev pseudo-spectral (CPS) method is presented for solving Troesch’s problem, which is a singular, highly sensitive, and nonlinear boundary problem and occurs in the consideration of the confinement of a plasma column by radiation pressure. Here, a continuous time optimization (CTO) problem corresponding to Troesch’s problem is first proposed. Then, the Chebyshev pseudo-spectral method is used to convert the CTO problem to a discrete-time optimization problem its optimal solution can be found by nonlinear programming methods. The feasibility and convergence of the generated approximate solutions are analyzed. The proposed method is used to solve various kinds of Troesch’s equations. The obtained results have been compared with approximate solutions resulting from well known numerical methods. It can be confirmed that the numerical solutions resulting from this method are completely acceptable and accurate, compared with other techniques. 
کلیدواژه‌ها
Troesch’s problem؛ Nonlinear programming؛ Chebyshev pseudo-spectral method؛ Continuous and discrete time optimization
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