A New Way to Generate an Exponential Finite Difference Scheme for 2D Convection-Diffusion EquationsReport as inadecuate




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Journal of Applied MathematicsVolume 2014 2014, Article ID 457938, 14 pages

Research ArticleSchool of Computer Science and Technology, Tianjin University, Tianjin 300072, China

Received 16 March 2014; Revised 27 May 2014; Accepted 28 May 2014; Published 29 June 2014

Academic Editor: Turgut Öziş

Copyright © 2014 Caihua Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The idea of direction changing and order reducing is proposed to generate an exponentialdifference scheme over a five-point stencil for solving two-dimensional 2D convection-diffusionequation with source term. During the derivation process, the higher order derivatives along y-direction are removed to the derivatives along x-direction iterativelyusing information given by the original differential equation similarly from x-direction toy-direction and then instead of keeping finite terms in the Taylor series expansion, infiniteterms which constitute convergent series are kept on deriving the exponential coefficientsof the scheme. From the construction process one may gain more insight into the relationsamong the stencil coefficients. The scheme is of positive type so it is unconditionallystable and the convergence rate is proved to be of second-order. Fourth-order accuracycan be obtained by applying Richardson extrapolation algorithm. Numerical resultsshow that the scheme is accurate, stable, and especially suitable for convection-dominatedproblems with different kinds of boundary layers including elliptic and parabolic ones. The idea of the method can be applied to a wide variety of differential equations.





Author: Caihua Wang

Source: https://www.hindawi.com/



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