A compact finite difference scheme with absorbing boundary condition for forced KdV equation.

Area of Science:

• Computational fluid dynamics
• Nonlinear partial differential equations
• Applied mathematics

Background:

• Simulating blood flow in arteries requires understanding the Korteweg-de Vries (KdV) equation.
• Accurate numerical methods are needed for solving forced KdV problems driven by periodic forces, like heart pulses.

Purpose of the Study:

• To develop and present an accurate numerical method for the forced KdV equation.
• To achieve fourth-order accuracy in approximating solutions.
• To ensure accurate simulation of wave propagation in long channels.

Main Methods:

• A compact finite difference scheme was developed for the forced KdV problem.
• An absorbing boundary condition was implemented to prevent wave reflection.
• Stability analysis was performed using the von Neumann method.

Main Results:

• The proposed compact finite difference scheme achieves fourth-order accuracy.
• The absorbing boundary condition effectively eliminates wave reflection.
• Numerical examples confirm the method's accuracy and stability.

Conclusions:

• The developed numerical method provides an accurate approximation for the forced KdV equation.
• The technique is suitable for simulating phenomena like pulsatile blood flow.
• The method ensures stable and non-reflective wave propagation.