Computational Solutions of Two Dimensional Convection Diffusion Equation Using Crank-Nicolson and Time Efficient ADI
| Autor: | D. S. Mashat, Shahid Hasnain, Muhammad Saqib |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Diffusion equation
Iterative method Mathematical analysis 010103 numerical & computational mathematics General Medicine 01 natural sciences Time efficient Term (time) 010101 applied mathematics Nonlinear system Alternating direction implicit method Crank–Nicolson method 0101 mathematics Convection–diffusion equation Mathematics |
| Zdroj: | American Journal of Computational Mathematics. :208-227 |
| ISSN: | 2161-1211 2161-1203 |
| DOI: | 10.4236/ajcm.2017.73019 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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