文章基本信息

标题：Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation
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作者：Asma Yosaf ; Shafiq Ur Rehman ; Fayyaz Ahmad 等
期刊名称：Advances in Numerical Analysis
印刷版ISSN：1687-9562
电子版ISSN：1687-9570
出版年度：2016
卷号：2016
DOI：10.1155/2016/8376061
出版社：Hindawi Publishing Corporation
摘要：The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D) heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary conditions. In the case of Dirichlet boundary conditions, the introduced parameter behaves like a free parameter and could take any value from its defined domain but for the Neumann boundary condition we obtained a particular value of the parameter. In both proposed compact finite difference methods, the order of accuracy is the same for all nodes. The time discretization is performed by using Crank-Nicholson finite difference method. The unconditional convergence of the proposed methods is presented. Finally, a set of 1D heat conduction equations is solved to show the validity and accuracy of our proposed methods.