AN APPROPRIATE IMPLEMENTATION OF THE BLOCK BY BLOCK METHOD FOR SOLVING NONLINEAR VOLTERRA INTEGRAL EQUATIONS IN LARGE INTERVALS

In this paper, we propose a block by block method with Romberg quadrature rule for solving Urysohn type Volterra integral equations effectively in large intervals. In fact, for each interval, we introduce a method with at least six order of convergence, that is, for the given step size h, we prove that the order of convergence is at lest h6. We give also numerical examples to clarify accuracy of the method.