Derivation of Continuous Linear Multistep Hybrid Block Method for the Solution of Volterra Integral Equation of Second Kind

In this paper, we proposed a continuous linear multistep hybrid block method for the solution of Volterra integral equation of second kind of the form y(x) = f (x) +

(x, s)y(s))ds, using power series and trigonometrically fitted function as the trial solution for the approximation via collocation techniques. The proposed hybrid block scheme is found to be consistent, zero-stable and convergent. The implementation of the scheme on numerical problems and comparisons of results obtained with existing numerical method will be included.