UNDER RECONSTRUCTION

1. by Dennis Darland dennis.darland@yahoo.com

   dennisdarland.com

   Comments welcome

2. December 12/12/2010
   I have abandoned this project.
   There are problems I am unable to solve and my mind is not working well.
   I intend to devote myself to philosophy - and may do some prolog programming fot that.
   
3. These Ruby programs generate programs in Maple or Ruby to solve Systems of Ordinary Differential Equations. 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. The Maple verion is gone as, at least for now, I do not have Maple available to me. I have started on a maxima version. In it I am taking time to remove some of the biggest inefficiencies. Also I may have found an error that I am trying to resolve. The Ruby version below would possibly also contain the error. But no one has reported any problems to me.
1. Coming soon here - a maxima version
2. There are problems with the Ruby and Maple versions which will have to wait until the maxima version is released.
4. Y. F. Chang's Draft Typescript(1978) on Taylor Series Chang on ATS
5. The Taylor series terms are used to calculate the values of the dependent variables, and also (optionally) the radius of convergence and order of any singularities. These can be used to reduce the size of the next increment. These can be used to reduce the size of the next increment. Increasing it in the middle results in large errors because each successive term is multiplied by increasing powers of the ratio of the new h to the old h. In the beginning I determine h by starting with a very small h and increase it until the estimated truncation error is as large as specified as permissible.
6. To visit the sourceforge project web page try Sode Project Page
7. For info on RubyApfp: RubyApfp Home Page