An accelerated iterative technique for solving mixed Fredholm-Volterra integral equations

In this paper, we propose an accelerated numerical technique for solving mixed Fredholm-Volterra integral equations (MFVIEs). The MFVIE is solved using the two-grid iterative technique, which uses a small system of equations to reach higher accuracy. The convergence analysis showed that using this technique reduces computational costs by 85% compared with the direct method. We introduce an algorithm to implement this method and numerical simulations are presented to verify the accuracy rate of the theoretical analysis.