New IIR digital differintegrators (differentiator and integrator) with very minor absolute relative errors are presented in this paper. The digital integrator is designed by interpolating some of the existing integrators. The optimum value of the interpolation ratio is obtained through linear programming optimization. Subsequently, by modifying the transfer function of the proposed integrator appropriately, new digital differentiator is obtained. Simulation results demonstrate that the proposed differintegrator are a more accurate approximation of ideal ones, than the existing differintegrators. Furthermore, the proposed differentiator has been tested in an image processing application. Edges characterize boundaries and are, therefore, a problem of fundamental importance in image processing. For comparison purpose Prewitt, Sobel, Roberts, Canny, Laplacian of Gaussian (LOG), Zerocross operators were used and their results are displayed. The results of edge detection by some of the existing differentiators are also provided. The simulation results have shown the superiority of the proposed approach over existing ones.