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.
Tsega, E. G (2024). Two-Dimensional Nonlinear Schrödinger Equation Using an Alternating Direction Implicit Method. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2024.61040.2619
MLA
Tsega, E. G. "Two-Dimensional Nonlinear Schrödinger Equation Using an Alternating Direction Implicit Method", Computational Methods for Differential Equations, , , 2024, -. doi: 10.22034/cmde.2024.61040.2619
HARVARD
Tsega, E. G (2024). 'Two-Dimensional Nonlinear Schrödinger Equation Using an Alternating Direction Implicit Method', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2024.61040.2619
CHICAGO
E. G Tsega, "Two-Dimensional Nonlinear Schrödinger Equation Using an Alternating Direction Implicit Method," Computational Methods for Differential Equations, (2024): -, doi: 10.22034/cmde.2024.61040.2619
VANCOUVER
Tsega, E. G Two-Dimensional Nonlinear Schrödinger Equation Using an Alternating Direction Implicit Method. Computational Methods for Differential Equations, 2024; (): -. doi: 10.22034/cmde.2024.61040.2619
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