EXTENDED BACKWARD DIFFERENTIATION FORMULAS IN THE NUMERICAL-SOLUTION OF GENERAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS

In this paper nonlinear Volterra integro-differential equations are co nsidered with kernels of the form P(x,s,y(s)) and K(x,s,y(x),y(s)) and extended backward differentiation methods are applied as extended fro m their introduction for the solution of ordinary differential equatio ns by Cash [4]. An error bound is obtained and a rate of convergence i s found and validated by testing the method on some examples. The nume rical results are compared with those obtained by applying standard ba ckward differentiation and collocation methods.