TITLE:
Computational Solutions of Two Dimensional Convection Diffusion Equation Using Crank-Nicolson and Time Efficient ADI
AUTHORS:
Muhammad Saqib, Shahid Hasnain, Daoud Suleiman Mashat
KEYWORDS:
Crank-Nicholson, Taylor’s Series, Newton’s Iterative Method, Alternating Direction Implicit (ADI)
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.3,
August
3,
2017
ABSTRACT: 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.