An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline...

Area of Science:

• Quantum Mechanics
• Fractional Calculus
• Numerical Analysis

Background:

• The time fractional Schrödinger equation is crucial for modeling complex quantum systems and anomalous diffusion.
• Fractional calculus offers advanced tools for describing non-classical physical phenomena.
• Cubic B-spline functions are effective in numerical analysis and computer graphics.

Purpose of the Study:

• To introduce an efficient numerical method for solving the time fractional Schrödinger equation.
• To utilize B-spline functions in conjunction with the Atangana-Baleanu fractional derivative.
• To analyze the method's accuracy and efficiency across various parameters.

Main Methods:

• A finite difference scheme was employed for temporal discretization of the Atangana-Baleanu fractional derivative.
• A θ-weighted scheme was used for spatial discretization.
• The numerical method was implemented using cubic B-spline functions.

Main Results:

• The proposed method demonstrates efficiency in solving the time fractional Schrödinger equation.
• Numerical results validate the method's performance.
• Error norms were systematically examined for different parameter values.

Conclusions:

• The B-spline based numerical method is effective for the time fractional Schrödinger equation.
• The study confirms the applicability of the Atangana-Baleanu fractional derivative in this context.
• The findings contribute to the numerical treatment of fractional differential equations in physics.