Stability analysis of the two-dimensional advection-diffusion equation for particle distribution by the Crank Nicolson-alternating direction implicit method

Particle distribution that occurs in waste stabilization ponds is a phenomenon that can be formulated using mathematics. The proposed model is a two-dimensional advection and diffusion model. We develop the model using differential equations that consider the x-axis and y-axis. We will solve the equation with the crank nicolson-alternating direction implicit finite difference method. the goal is to show the stability analysis of the method used to solve the proposed model. The results obtained show that the method used obtains unconditional stability.