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The main goal of this paper is to obtain error bounds for parabolic integro-differential equation. The derivation of these bounds is based elliptic and Ritz -Volterra reconstructions introduced by Makridakis and Nochetto 2003 and then extended to Ritz - Volterra reconstruction in case of integro-parabolic differential problems by Reddy and Sinha 2015. We proved optimal order bounds for certain classes semilinear parabolic intergro differential equations. The key points for these estimators can be reduced the numbers of iterations.

Posteriori Error bound For Fullydiscrete Semilinear Parabolic Integro-Differential equations