基于Web的微分方程自动求解系统的研究与开发

发布时间：2018-01-11 08:15

本文关键词：基于Web的微分方程自动求解系统的研究与开发　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：微分方程在现代科技、工程领域中的作用日益显著,本课题组与同行多年来在微分方程可积性和解析求解方面做了很多机械化工作,研发出了一系列Maple应用软件。基于这些应用软件、计算机代数系统Maple及一些开源技术,本文研发了一个在线的开放的微分方程自动求解系统NDEmathema,为用户提供了便捷的代数计算和绘图服务。NDEmathema计算系统采用了 B/S架构,本文中还将详细阐述了它的组成结构、设计原理。在此计算系统中,用户不仅可调用已嵌入的Maple外部应用软件求解微分方程和代数方程(组),而且可在交互方式下进行几乎所有和方程相关的简单符号计算,一般的计算结果均以二维数学公式的形式输出,有些结果以图片方式展示。该计算系统的主要亮点为数学公式的在线可视化显示。另外,计算系统NDEmathema也实现了跨浏览器、跨设备和跨操作系统平台等功能,具有较强的应用价值。本文的研究工作具体包括:(1)主流符号计算软件的集成方法的研究从底层研发计算系统费时费力,为了节省时间,我们以主流符号计算系统为底层,从应用入手开展研发工作。我们首先对Maple,Maxima,Mathematica等主流符号计算软件在命令行下的接口进行了深入研究,接着熟悉了具体的调用方法,特别是对Maple,Maxima的集成方法已完全掌握。(2)基于Web的针对微分方程的自动求解系统的设计和实现研发在线计算系统NDEmathema,我们选取了 B/S架构,并对B/S架构下的相应技术进行了详细分析,进而设计了合理的模块结构,在具体的开发中我们还使之保持着良好的扩展性,以便后续增加新功能。(3)将数学公式的在线可视化技术应用到计算系统中的研究数学公式的输入、存储和显示是我们研发过程中的一个重点内容,我们应用开源技术ASCIIMathML和MathJax显示二维数学公式,并制定了所需的详细转换规则。在NDEmathema中,输出的计算结果中的数学公式以文本形式存储,显示时转换成二维数学公式。该显示方法兼容各种浏览器,并支持公式的移植和复用。(4)演算过程和计算结果的导出和离线管理方法的研究为了方便用户保存和后续使用在线演算过程或计算结果,我们研究了将NDEmathema计算系统求解问题时的演算过程和计算结果进行导出和离线管理的方法。熟悉Maple软件的用户可以将NDEmathema的演算过程和计算结果导出为Maple的Worksheet文档供后续管理和使用,而不熟悉Maple软件的用户可以将其导出为HTML文件。
[Abstract]:Differential equations play an increasingly important role in the field of modern technology and engineering. Our team and peers have done a lot of mechanized work on the integrability and analytical solution of differential equations for many years. A series of Maple applications have been developed. Based on these applications, the computer algebra system Maple and some open source technologies have been developed. In this paper, an online open differential equation automatic solution system, NDEmathema, is developed. It provides a convenient algebraic computing and drawing service. NDEmathema computing system adopts the B / S architecture. In this paper, the composition of the system is described in detail. Design principle. In this computing system, the user can not only call the embedded Maple external application software to solve differential equations and algebraic equations (sets). Moreover, almost all the simple symbolic calculations related to the equation can be carried out in the interactive mode, and the general results are all output in the form of two-dimensional mathematical formulas. Some of the results are displayed in the form of pictures. The main highlight of this computing system is the online visualization of mathematical formulas. In addition, the computing system NDEmathema also implements cross-browser. Cross-device and cross-operating system platform and other functions have strong application value. The research work of this paper includes the research of integration method of mainstream symbolic computing software from the bottom of the research and development of computing system time-consuming and laborious. In order to save time, we take the mainstream symbolic computing system as the bottom layer, start with the research and development work from the application. Mathematica and other mainstream symbolic computing software in the command line interface in-depth study, and then familiar with the specific methods of calling, especially to the Maple. The integration method of Maxima has been fully mastered. (2) the design and implementation of an automatic solution system for differential equations based on Web (NDEmathema). We select the B / S architecture, and the corresponding technology under the B / S architecture is analyzed in detail, and then we design a reasonable module structure, in the specific development we also maintain a good scalability. In order to add a new function in the future, the on-line visualization technology of mathematical formula is applied to the research of mathematical formula input, storage and display is an important content in our R & D process. We use the open source techniques ASCIIMathML and MathJax to display two-dimensional mathematical formulas and work out the required detailed transformation rules in NDEmathema. The mathematical formula of the output calculation result is stored in the form of text and converted into two-dimensional mathematical formula when displayed. The display method is compatible with various browsers. It also supports the transplantation of formulas and the derivation of calculation results and the study of off-line management methods for the convenience of users to save and use online calculus process or calculation results. In this paper, we study the derivation and off-line management of the calculation process and results of NDEmathema computing system. Users who are familiar with Maple software can use NDEmath to solve the problem. The ema calculus and results are exported as Maple's Worksheet documents for subsequent management and use. Users who are unfamiliar with Maple software can export it as HTML files.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP311.52

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