NUMERICAL SOLUTIONS OF DIFFUSION AND DIFFUSION-CONVECTION EQUATIONS

An important question concerning computational solutions is what guarantee can be given that the computational solution will be close to the exact solution of the partial differential equation(s), and under what circumstances the computational solution wiThe numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, The aim of this work is to investigate the numerical solution of convection-diffusion-reaction equation. The solutions of the one and two dimensional problems are discussed in two cases: Firstly, we usethe implicit scheme, namely alternating-direction-impliciy (ADI) scheme which originally proposed by Peaceman and Rachford . The solution is based on the well known discretization scheme, which is applied at any stage of (ADI) scheme steps. We approximateA formulation of (ADI) method is given by extending Peaceman and Rachford scheme to three dimensions. The scheme becomes conditionally stable. The Von Neumann stability analysis is performed. Numerical results for solving the heat diffusion equation have