Solving dynamical nonlinear problem with Ck spline functions and Grobner bases techniques: an example

We describe a method to solve the differential equations involved in a dynamical nonlinear problem with C^k spline functions and their algebraic properties. Spline functions generate k time continuous and derivable approximations. These functions seem to be very efficient in several applied nonlinear differential problems. The computation of these functions use the algebraic methods known as Grobner bases, which are more robust, more precise and often more efficient than the purely numerical methods. An example on solving nonlinear differential equations using these methods is presented.