Application of Collocation Methods for a Hybrid Block Scheme for the Solution of Volterra Intregral Equation of the Second Kind

In this paper, a class of three-step implicit second order hybrid block methods for the solutions of Volterra integral equation of the second kind has been developed, using the interpolation and collocation approach. The discrete block methods were recovered when the continuous block methods were evaluated at all step points. The block methods used to implement the main method guaranteed that each discrete scheme obtained from the simultaneous solution of the block has the same order of accuracy as the main continuous method. Hence, the new class of k-step methods gives high order of accuracy with very low error. The basic properties of the methods were investigated and the methods were found to be consistent, zero-stable and convergent.