Effective Local Absorbing Boundary Conditions for a Finite Difference Implementation of the Parabolic Equation

Domain truncation by transparent boundary conditions for open problems where parabolic equation is utilized to govern wave propagation are in general computationally costly. We utilize two approximations to a convolution-in-space type discrete boundary condition to reduce the cost, while maintaining accuracy in far range solutions. Perfectly matched layer adapted to the Crank-Nicolson finite difference scheme is also verified for a 2-D model problem, where implemented results and stability analyses for different approaches are compared.