Author(s)

Muhammad Saqib, Shahid Hasnain, Daoud Suleiman Mashat

Department of Mathematics, Numerical Analysis, King Abdulaziz University, Jeddah, Saudi Arabia.

To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The procedure was combined with Iterative methods to solve non-linear systems. Efficiency and accuracy are studied in term of L₂, L∞ norms confirmed by numerical results by choosing two test examples. Numerical results show that proposed alternating direction implicit scheme was very efficient and reliable for solving two dimensional nonlinear convection diffusion equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.

Crank-Nicholson, Taylor’s Series, Newton’s Iterative Method, Alternating Direction Implicit (ADI)

Saqib, M. , Hasnain, S. and Mashat, D. (2017) Computational Solutions of Two Dimensional Convection Diffusion Equation Using Crank-Nicolson and Time Efficient ADI. American Journal of Computational Mathematics, 7, 208-227. doi: 10.4236/ajcm.2017.73019.