Research And Development Of Web-Based Automated Computing System For Differential Equations

Differential equations are playing more and more important role in modern science,technologies and engineering.On solving and integrability analysis of differential equations,our research group and peers have done a lot of work in aspects of mathematics mechanization,and developed a series of different related off-line software based on Maple.On the basis of these Maple packages,Maple and some open-source technologies,an online automated computing system for differential equations called NDEmathema was developed.NDEmathema can provide convenient and efficient online computing and graphing services for users.NDEmathema has a B/S architecture,while its structure and design principles will be demonstrated in this dissertation in detail.On this computing system,users can not only solve differential and algebraic equations using external Maple packages,but also execute almost all simple symbolic computations related to equations in the interactive mode.For each input,in a general case,NDEmathema outputs the computing results in two-dimensional form,while some computing results are shown as images.The main strength of the computing system NDEmathema is displaying mathematical formulas online visually.In addition,the computing system also has the features of cross-browser,cross-device and cross-operating system platform.Besides,it has strong practical value.The main content of our research work is listed as follows.(1)Research on integration methods of popular symbolic computing softwareDeveloping symbolic computing software from the ground has a high time cost.In order to save time,we started developing a Web-based automated computing system based on the polpular symbolic computing software and their applications.Firstly,we studied deeply to the interfaces of the popular symbolic computing software such as Maple,Maxima and Mathematica under the command-line mode.Among them,we are especially familiar with the methods of calling Maple and Maxima,and we have mastered integration method of them completely.(2)Design and implementation of Web-based automated computing system for differential equationsIn order to develop the Web-based automated computing system NDEmathema,we choose the B/S architecture and analyze the corresponding technologies under B/S architecture.In addition,we have designed a reasonable module structure.In the concrete development,we also remain the computing system with well extensity,so that new functions can be added easily.(3)Research on applying the online visual display technologies of mathematical formulas to the computing systemThe input,storage and displaying of mathematical formulas is a crucial part of our research and development.The open source technologies ASCIIMathML and MathJax are applied to the online computing system for displaying mathematical formulas in two-dimensional form.In order to apply them successfully,we created concrete conversion rules.In the visual output results of NDEmathema,the mathematical formulas are stored in text form,but they are converted into two-dimensional mathematical formulas when displayed online.The method we adopted to display mathematical formulas is compatible with all kinds of browsers,and it supports transplantation and reuse of mathematics formulas.(4)Research on exporting and off-line management methods of the calculating process and computing resultsIn order to provide users with saving and later use of online calculating process and computing results,we have studied exporting and off-line management methods of the calculating process and computing results from the computing system NDEmathema when solving the problem.Users who are familiar with Maple software can export the calculating process and computing results of NDEmathema as Maple's Worksheet documents for later management and use,and users who are not familiar with Maple software can export them as HTML files.