On a rational differential quadrature method in irregular domains for problems with boundary layers

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• 作者：Liangliang  ; Du ; Xionghua  ; Wu  ; ;   ; ^{wuxh@tongji.edu.cn}
• 关键词：Irregular domains ; Rational differential quadrature method ; Singularly perturbed problems ; Boundary layer ; Direct expansion method
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：15 October 2011
• 年：2011
• 卷：218
• 期：4
• 页码：1379-1388
• 全文大小：591 K

文摘

A rational differential quadrature method in irregular domains (RDQMID) is investigated to deal with a kind of singularly perturbed problems with boundary layers. Through a transformation, the boundary layer, which may be not straight, is transformed into a segment of a line parallel to one of the Cartesian axes. The rational differential quadrature method (RDQM) is applied to discretize the governing equation. Finally, a direct expansion method of the boundary conditions (DEMBC) is raised to deal with the boundary conditions. Numerical experiments show that RDQMID is of high accuracy, efficiency and easy to programme.