I have as a project to write some software for solving an equation numerically. Fortunately I am working on an equation that was already solved and so I know the starting place and the ending place however I don't have a great deal of experience with doing anything more complicated than basic numeric solutions like Newton's method or Euler's method that I did years ago in undergraduate school. There is so much information out there I am getting a little overwhelmed with where to begin. I was wondering if anyone had experience in doing this. My coding skills are passable but not fantastic. Mostly I am looking for guidance on modern techniques used, background in scientific computing and any other suggestions people with more experience have for tackling this problem. Any papers people have found useful or books would also be great. Thank you.

Regards,
Caleb

There's a lot of information because no one system is good at finding all solutions. More detail is required for advice. How many dimensions (variables) to the problem? Is it analytic or defined by tables?