Erhan, İ. M., & Wlie, S. M. (2023). Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 66–80.
- ISSN: 2587-2648
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İnci M. Erhana, Saeida M. Wileb
aDepartment of Computer Engineering, Aydın Adnan Menderes University, 09010, Aydın, Türkiye
bDepartment of Mathematics, Faculty of Arts and Science, Mesllata, Elmergib University, Libya
In this study, we introduce the pseudospectral methods based on Chebyshev and Legendre polynomials for the Schrödinger equation of anharmonic oscillator. The method transforms the problem into an unsymmetric matrix eigenvalue problem which can be symmetrized by using a suitable similarity transformation. Computation of the zeros of the relevant orthogonal polynomials is also converted into a symmetric matrix eigenvalue problem. The method is applied to the Schrödinger equation of an anharmonic oscillator of various types and the numerical results are discussed.
Keywords: Schrödinger equation; Pseudospectral method; Chebyshev polynomial; Legendre polynomial.
Erhan, İ. M., & Wlie, S. M. (2023). Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods. Advances in the Theory of Nonlinear Analysis and Its Application, 7(5), 66–80.