Numerical methods for solving nonlinear Volterra integro-differential equations based on Hermite–Birkhoff interpolation

We introduce a new family of multivalue and multistage methods based on Hermite–Birkhoff interpolation for solving nonlinear Volterra integro differential equations. The proposed methods that have high order and ex tensive stability region, use the approximated values of the first derivative of the solution in the m collocation points and the approximated values of the solution as well as its first derivative in the r previous steps. Convergence order of the new methods is determined and their linear stability is analyzed. Efficiency of the methods is shown by some numerical experiments.

Keywords:

Volterra integro-differential equations , Multistep collocation methods , Hermite–Birkhoff interpolation , Convergence , Linear stability