Approximate solutions to differential equations through polynomial interpolation.

[mardlamock]

Absolutely. What you are looking for is called the Collocation Method. Very frequently, the numerical solution will use a Collocation Method as a single step in an implicit RK scheme. But if you are working with compact space and you expect polynomial of sufficient degree to be a good approximation to true solution, you can just collocate the entire space and do this in one go.

Unfortunately, general collocation method requires solving a non-linear optimization problem. However, in a special case where you are solving y'(x) = f(x), the collocation can be solved analytically. But then you are really just doing numerical integration and your analytical solution is the quadrature rule for your collocation points.

For solutions approximated with polynomials, Gauss-Legendre quadrature points are a good choice for collocation points.

THANK YOU! Im not so crazy after all! You just made me happy, I feel smart now. I ll see if I can do it on excel, still struggling with matlab

Edited April 7, 2015 by mardlamock