Numerical results and stability of ADI method to two-dimensional advection-diffusion equations with half step of time

PRISMA, Prosiding Seminar Nasional Matematika
Vol 5 (2022): PRISMA, Prosiding Seminar Nasional Matematika XV

We are concerned with the study of stability and numerical results of discretization for alternating direct implicit (ADI) method to two-dimensional advection-diffusion equation. We first discrete two-dimensional advection-diffusion by using forward difference of time and central difference of space. Then, we have two matrices with the step size of time and , in which this technique is the idea of ADI method. The stability is established by using the Von-Neumann stability technique where the stability characteristic of ADI method is unconditionally stable.