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 an 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 that its optimal solution can be find 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 equation. The obtained results have been compared with approximate solutions resulted from well-known numerical methods. It can be confirmed that the numerical solutions resulted from this method are completely acceptable and accurate, compared with other techniques.
Ghaznavi, M., & Noori Skandari, M. H. (2024). A Chebyshev pseudo-spectral based approach for solving Troesch's problem with convergence analysis. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2024.56313.2355
MLA
Mehrdad Ghaznavi; Mohammad Hadi Noori Skandari. "A Chebyshev pseudo-spectral based approach for solving Troesch's problem with convergence analysis". Computational Methods for Differential Equations, , , 2024, -. doi: 10.22034/cmde.2024.56313.2355
HARVARD
Ghaznavi, M., Noori Skandari, M. H. (2024). 'A Chebyshev pseudo-spectral based approach for solving Troesch's problem with convergence analysis', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2024.56313.2355
VANCOUVER
Ghaznavi, M., Noori Skandari, M. H. A Chebyshev pseudo-spectral based approach for solving Troesch's problem with convergence analysis. Computational Methods for Differential Equations, 2024; (): -. doi: 10.22034/cmde.2024.56313.2355
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