Systems of Ordinary Differential Equations

Systems of Ordinary Differential Equations RubySode (Sode.rb) is a Ruby program to generate a Ruby program to solve a single (or a system of) ordinary differential equation(s). A long Taylor series method, pioneered by Prof. Y.F. Chang, who taught at the University of Nebraska in the late 1970's when I was a graduate student there, is used.

The number of Taylor series terms can be specified in the problem file, though it is usually 30.

What is new in this release:

• The results are now summarized in table.html, which has links to the files specifying the problems, the programs generated, and the results of running the programs.
• A new program now detects the operating system (and asks if it cannot tell) and asks which languages to use (C, C++, Ruby, Maxima, or Maple) and the name of an odes file listing the problems specified in ode files to be solved.
• The generated table makes it easier to inspect the results.
• Comparison can be made to closed form solutions of the differential equations if they are available.

What is new in version 0030:

• This version adds support for Si and erf functions for Maple only.

What is new in version 0029:

• This version supports Windows, although just for Ruby.
• It may generate code that is basically correct for C,C++, and Maple for Windows, but the author doesn't have those languages.

What is new in version 0027:

• This version adds much more thorough testing.
• Numerous bugs have been fixed.

What is new in version 0018:

• This version supports negative increment.
• A display interval may be set.

What is new in version 16:

• This version supports generating C in addition to C++, Maple, and Maxima.
• It supports local declarations in problem definition files for maxima.
• It reports digits (16) for C and C++. correctly.
• It reports correct digits if an analytic solution is provided.
• The order of rows in the results table has been reversed (now alphabetical).