基于Python求解偏微分方程的有限差分法.pdfVIP

·14 · Computer Era No. 11 2016 DOI: 10.16644/33-1094/tp.2016.11.005 基于Python求解偏微分方程的有限差分法* 王登岳，张宏伟 (西安石油大学电子工程学院光电油气测井与检测教育部重点实验室，陕西 西安 710065) 摘 要：偏微分方程的求解是很多科学技术问题的关键难点。随着计算机性能的不断提高，数值解法能够解复杂的偏 微分方程并将计算结果图形化。相对于昂贵的科学计算软件，Python 是一种免费的面向对象、动态的程序设计语言。有 限差分法以其概念清晰，方法简单、直观等特点在偏微分方程的求解中得到了广泛的应用。文章对矩形区域的拉普拉斯 方程进行数值求解，采用Numpy 对有限差分法进行计算，运用Matplotlib 绘制等值线，输出迭代次数以及误差。 关键词：偏微分方程；Python ；数值解法；有限差分法 中图分类号：TP3 文献标志码：A 文章编号：1006-8228(2016)11-14-03 Python programmed finite difference method for solving partial differential equations Wang Dengyue, Zhang Hongwei （XianShiyouUniversity,ElectricEngineeringCollege, KeyLaboratory of Photo ElectricityGasandOil Detecting of Ministry of Education, Xian, Shaanxi 710065, China） Abstract ：To solve the partial differential equations (PDE) is a key difficult point in many scientific and technical problems. With the development of computer performance, numeric solution can solve many sophisticated PDE and visualize the numeric results. Rather than the expensive science computing software, Python is a free object-oriented language, dynamic programming language. Finite difference method (FDM) is widely used for its clear, simple and intuitive. Laplace problem in a rectangular area is solved numerically in the article, computed through FDM with the Numpy library, visualized through plotting the contour by the Matplotlib library, and the number of iteration and the error are given. Key words ：partial difference equation ；Python ；numeric solution ；finite difference method 0 引言 序库的开发，Python同样适合于做科学计算以及绘制 在数学中，偏微分方程是包含多变量和它们的偏 高质量的2D和3D图像。与科学计算领域的商业软件