MULTISTEP COLLOCATION METHODS BASED SINGULAR KERNELSON PRODUCT INTEGRATION FOR SOLVING SECOND KIND VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY

In this paper, we construct multistep collocation methods for solving nonlinear weakly singular Volterra integral equations. In every subinterval, the kernel of integral equation is approximated by r previous time steps and m collocation points in the current subinterval. Then substituting this approximate and using product integration, the Nystrom type interpolation for approximating of the solution is obtained. Order of convergence is determined and efficiency of the method is shown by some numerical examples.