Spline Collocation for Volterra - Fredholm Integro-Differential Equations

A collocation procedure is developed for the linear and nonlinear Volterra - Fredholm integro-differential equations, using the globally defined B-spline and auxiliary basis functions. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically.

Keywords:

Volterra-Fredholm integro-differential equations , Cubic B-spline Newton-Cotes formula , Convergence analysis