本文關(guān)鍵詞：基于Web的微分方程自動求解系統(tǒng)的研究與開發(fā)　出處：《華東師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

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【摘要】：微分方程在現(xiàn)代科技、工程領(lǐng)域中的作用日益顯著,本課題組與同行多年來在微分方程可積性和解析求解方面做了很多機(jī)械化工作,研發(fā)出了一系列Maple應(yīng)用軟件。基于這些應(yīng)用軟件、計(jì)算機(jī)代數(shù)系統(tǒng)Maple及一些開源技術(shù),本文研發(fā)了一個在線的開放的微分方程自動求解系統(tǒng)NDEmathema,為用戶提供了便捷的代數(shù)計(jì)算和繪圖服務(wù)。NDEmathema計(jì)算系統(tǒng)采用了 B/S架構(gòu),本文中還將詳細(xì)闡述了它的組成結(jié)構(gòu)、設(shè)計(jì)原理。在此計(jì)算系統(tǒng)中,用戶不僅可調(diào)用已嵌入的Maple外部應(yīng)用軟件求解微分方程和代數(shù)方程(組),而且可在交互方式下進(jìn)行幾乎所有和方程相關(guān)的簡單符號計(jì)算,一般的計(jì)算結(jié)果均以二維數(shù)學(xué)公式的形式輸出,有些結(jié)果以圖片方式展示。該計(jì)算系統(tǒng)的主要亮點(diǎn)為數(shù)學(xué)公式的在線可視化顯示。另外,計(jì)算系統(tǒng)NDEmathema也實(shí)現(xiàn)了跨瀏覽器、跨設(shè)備和跨操作系統(tǒng)平臺等功能,具有較強(qiáng)的應(yīng)用價值。本文的研究工作具體包括:(1)主流符號計(jì)算軟件的集成方法的研究從底層研發(fā)計(jì)算系統(tǒng)費(fèi)時費(fèi)力,為了節(jié)省時間,我們以主流符號計(jì)算系統(tǒng)為底層,從應(yīng)用入手開展研發(fā)工作。我們首先對Maple,Maxima,Mathematica等主流符號計(jì)算軟件在命令行下的接口進(jìn)行了深入研究,接著熟悉了具體的調(diào)用方法,特別是對Maple,Maxima的集成方法已完全掌握。(2)基于Web的針對微分方程的自動求解系統(tǒng)的設(shè)計(jì)和實(shí)現(xiàn)研發(fā)在線計(jì)算系統(tǒng)NDEmathema,我們選取了 B/S架構(gòu),并對B/S架構(gòu)下的相應(yīng)技術(shù)進(jìn)行了詳細(xì)分析,進(jìn)而設(shè)計(jì)了合理的模塊結(jié)構(gòu),在具體的開發(fā)中我們還使之保持著良好的擴(kuò)展性,以便后續(xù)增加新功能。(3)將數(shù)學(xué)公式的在線可視化技術(shù)應(yīng)用到計(jì)算系統(tǒng)中的研究數(shù)學(xué)公式的輸入、存儲和顯示是我們研發(fā)過程中的一個重點(diǎn)內(nèi)容,我們應(yīng)用開源技術(shù)ASCIIMathML和MathJax顯示二維數(shù)學(xué)公式,并制定了所需的詳細(xì)轉(zhuǎn)換規(guī)則。在NDEmathema中,輸出的計(jì)算結(jié)果中的數(shù)學(xué)公式以文本形式存儲,顯示時轉(zhuǎn)換成二維數(shù)學(xué)公式。該顯示方法兼容各種瀏覽器,并支持公式的移植和復(fù)用。(4)演算過程和計(jì)算結(jié)果的導(dǎo)出和離線管理方法的研究為了方便用戶保存和后續(xù)使用在線演算過程或計(jì)算結(jié)果,我們研究了將NDEmathema計(jì)算系統(tǒng)求解問題時的演算過程和計(jì)算結(jié)果進(jìn)行導(dǎo)出和離線管理的方法。熟悉Maple軟件的用戶可以將NDEmathema的演算過程和計(jì)算結(jié)果導(dǎo)出為Maple的Worksheet文檔供后續(xù)管理和使用,而不熟悉Maple軟件的用戶可以將其導(dǎo)出為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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP311.52

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