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Numerical Solution of Linear and Nonlinear Schrödinger Equation via Shifted Chebyshev Collocation Method | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 دی 1403 اصل مقاله (1.36 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.57475.2405 | ||
| نویسندگان | ||
| Nidhi Prabhakar؛ Seema Sharma* | ||
| Department of Mathematics and Statistics, Gurukul Kangri (Deemed to be University), Haridwar, Uttarakhand. | ||
| چکیده | ||
| The present study focuses on numerical solutions of linear and nonlinear Schrödinger equation subject to initial and boundary conditions employing shifted Chebyshev spectral collocation method (SCSCM). In the solution procedure, unknown function and its space derivatives have been approximated employing shifted Chebyshev polynomials and their derivatives, respectively, together with Chebyshev-Gauss-Lobatto points. The present collocation method transforms Schrödinger equation into a system of ordinary differential equations (ODEs). Thereafter, obtained system has been solved employing fourth order Runge-Kutta scheme. In order to demonstrate accuracy and efficiency of the present method, a comparison of present numerical solutions of different examples of Schrödinger equation with exact and approximate solutions available in literature has been discussed. The SCSCM can be implemented to solve second and higher order linear and nonlinear partial differential equations (PDEs) arising in physics, mechanics and biophysics. | ||
| کلیدواژه‌ها | ||
| Shifted Chebyshev polynomials؛ Spectral collocation method, Schrödinger equation؛ Runge-Kutta method | ||
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آمار تعداد مشاهده مقاله: 113 تعداد دریافت فایل اصل مقاله: 114 |
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