کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9506339 1631840 2005 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A parameter-uniform implicit difference scheme for solving time-dependent Burgers' equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A parameter-uniform implicit difference scheme for solving time-dependent Burgers' equations
چکیده انگلیسی
A numerical study is made for solving one dimensional time dependent Burgers' equation with small coefficient of viscosity. Burgers' equation is one of the fundamental model equations in the fluid dynamics to describe the shock waves and traffic flows. For high coefficient of viscosity a number of solution methodology exist in the literature [6], [7], [8], [9] and [14] but for the sufficiently low coefficient of viscosity, the exist solution methodology fail and a discrepancy occurs in the literature. In this paper, we present a numerical method based on finite difference which works nicely for both the cases, i.e., low as well as high viscosity coefficient. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on uniform mesh and a standard upwind finite difference scheme to discretize in spacial direction on piecewise uniform mesh. The quasilinearzation process is used to tackle the non-linearity. An extensive amount of analysis has been carried out to obtain the parameter uniform error estimates which show that the resulting method is uniformly convergent with respect to the parameter. To illustrate the method, numerical examples are solved using the presented method and compare with exact solution for high value of coefficient of viscosity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 170, Issue 2, 15 November 2005, Pages 1365-1393
نویسندگان
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