High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

• 作者: Alemayehu Shiferaw Ramesh Chand Mittal
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Poisson’s EQUATION Tri-Diagonal Matrix FOURTH-ORDER Finite DIFFERENCE APPROXIMATION Hockney’s Method Thomas Algorithm
• 年，卷（期）: 2014,（2）
• 页码范围: 73-86
• 页数: 14页
• 分类号: O1

摘要

In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.