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Tsega, Endalew. (1404). Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method. سامانه مدیریت نشریات علمی, 13(3), 1012-1021. doi: 10.22034/cmde.2024.61040.2619
Endalew G Tsega. "Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method". سامانه مدیریت نشریات علمی, 13, 3, 1404, 1012-1021. doi: 10.22034/cmde.2024.61040.2619
Tsega, Endalew. (1404). 'Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method', سامانه مدیریت نشریات علمی, 13(3), pp. 1012-1021. doi: 10.22034/cmde.2024.61040.2619
Tsega, Endalew. Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method. سامانه مدیریت نشریات علمی, 1404; 13(3): 1012-1021. doi: 10.22034/cmde.2024.61040.2619

Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method

Computational Methods for Differential Equations
مقاله 20، دوره 13، شماره 3، مهر 2025، صفحه 1012-1021    اصل مقاله (995.08 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61040.2619
نویسنده
Endalew G Tsega*
Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia.
چکیده
In this paper, an alternating direction implicit (ADI) finite difference scheme is proposed for solving the two-dimensional time-dependent nonlinear Schrödinger equation. In the proposed scheme, the nonlinear term is linearized by using the values of the wave function from the previous time level at each iteration step. The resulting block tridiagonal system of algebraic equations is solved using the Gauss-Seidel method in conjunction with sparse matrix computation. The stability of the scheme is analyzed using matrix analysis and is found to be conditionally stable. Numerical examples are presented to demonstrate the efficiency, stability, and accuracy of the proposed scheme. The numerical results show good agreement with exact solutions.
کلیدواژه‌ها
Nonlinear Schrödinger equation؛ Time-dependent؛ Two-dimensional؛ ADI method؛ Block tridiagonal system؛ Sparse matrix؛ Gauss-Seidel method
مراجع
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