A shooting method for singular nonlinear second order Volterra integro-differential equations (Q1365291)

The method of parallel shooting is employed to solve a class of nonlinear second-order singular Volterra integro-differential equations with two-point boundary conditions of the form \[ y''= f(x,y,z),\quad 0\leq x\leq a,\quad y(0)= A,\quad y(a)= B, \] where \[ z(x)= \int^x_0 K(x,t,y(t))dt. \] The present work is related to the earlier work of the authors [Int. J. Comput. Math. 49, No. 1-2, 61-66 (1993; Zbl 0797.65113)]. A numerical example is given to illustrate the method developed in the paper.