Deviation of the error estimation for Volterra integro-differential equations

Abstract

In this paper, we study an efficient asymptotically correction of a-posteriori error estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro-differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O(hm+1) as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.