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

Document Type : Research Paper

Authors

Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.

Abstract

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. 

Keywords

Main Subjects

References

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Computational Methods for Differential Equations
Volume 12, Issue 4
October 2024
Pages 827-841

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History

  • Receive Date: 24 April 2023
  • Revise Date: 26 July 2023
  • Accept Date: 16 April 2024

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