Two-Dimensional Nonlinear Schrödinger Equation Using an Alternating Direction Implicit Method

Document Type : Research Paper

Author

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

Abstract

This paper introduces an alternating direction implicit (ADI) finite difference method to solve the two-dimensional time-dependent nonlinear Schrödinger equation. The method involves linearizing the nonlinear term by utilizing the wave function values from the previous time step at each iteration. The resulting block tridiagonal system of equations is solved using the Gauss-Seidel method through sparse matrix computation. Stability analysis employing matrix techniques reveals the scheme to be conditionally stable. Numerical examples are provided to demonstrate the effectiveness, stability, and accuracy of the proposed numerical approach. The computed results are in good agreement with exact solutions, further confirming the validity of the proposed method.

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Articles in Press, Accepted Manuscript
Available Online from 18 August 2024
  • Receive Date: 30 March 2024
  • Revise Date: 13 July 2024
  • Accept Date: 13 August 2024