An Improved ADI-DQM Based on Bernstein Polynomial for Solving Two-Dimensional Convection-Diffusion Equations

Abstract

In this article, we presented an improved formulations based on Bernstein polynomial in calculate the weighting coefficients of DQM and alternating direction implicit-differential quadrature method (ADI-DQM) that is presented by (Al-Saif and Al-Kanani (2012-2013)), for solving convection-diffusion equations with appropriate initial and boundary conditions. Using the exact same proof for stability analysis as in (Al-Saif and Al-Kanani 2012-2013), the new scheme has reasonable stability. The improved ADI-DQM is then tested by numerical examples. Results show that the convergence of the new scheme is faster and the solutions are much more accurate than those obtained in literature.

Keywords: Differential quadrature method, Convection-diffusion, Bernstein polynomial, ADI, Accuracy.