From data to ODEs on the Web: how can it be done and shown for execution ?

Abstract

Fitting systems of ordinary differential equations (ODEs) to experimental data is a common task in Engineering.  In the case of Chemical Engineering, this underlies chemical kinetics, addressed in this work.  The ODEs studied are systems of (two or more) explicit equations of a single variable, time.  The problem is a regression to determine the values of the parameters in the system.  Here, we select the ‘function’ in the assumed Python module, solve the problem, and provide a freely accessible web page where data can be inserted.  Thus:  we offer the computation, based on Python tools, in a web page;  we select the ‘function’, circumventing ‘curve_fit’ in favor of ‘minimize’;  we use PHP on the web page to call Python, with the ‘gnuplot’ graphing utility;  and we stress the Internet as a computing medium.  The computation runs on the server side, avoiding, from the user, any software installation, special power or operating system match.  This Web operation, which runs on a Linux platform, is also an illustration for many other problems.  Generally, about web computing, we advocate  (i) its use in web pages, where it employs programs similar to classical ones, the programs being the inevitable difficulty,  and (ii) its use in scientific publications.  In our technological era, this seemingly little explored field also promotes the academia industry link and invites knowledge interchange.