Abstract: Consider the Gregory integration (G) formula
with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by
minimizing some of the coefficient k a in the remainder term by
particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.
Abstract: In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations