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

Tsega, Endalew G

doi:10.22034/cmde.2024.61040.2619

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

Document Type : Research Paper

Author

Endalew G Tsega

Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia.

10.22034/cmde.2024.61040.2619

Abstract

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.

Keywords

Main Subjects

Numerical Analysis

References

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