University of Tabriz Computational Methods for Differential Equations 2345-3982 12 4 2024 09 01 A Chebyshev pseudo-spectral based approach for solving Troesch’s problem with convergence analysis 827 841 17805 10.22034/cmde.2024.56313.2355 EN Mehrdad Ghaznavi Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran. Mohammad Hadi Noori Skandari Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran. Journal Article 2023 04 24 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.  https://cmde.tabrizu.ac.ir/article_17805_cb5e503560e55c66e9c2cb5e7e7d1f83.pdf