Numerical solution of mixed Volterra-Fredholm integral equations using different methods

This study discusses the existence and unique solution of the second-kind mixed Volterra-Fredholm integral equation (MV-FIE). Using the projection approach, the best approximate solution can be found by providing two consecutive algorithms and primarily relying on the iterative projection process (P-IM). For every algorithm, we obtain the relative error and the approximate solution. Furthermore, we proved that the first algorithm's estimated P-IM error is better than the successive approximation method's (SAM) estimate. The error estimate was determined, and numerical results were calculated for each example. Some numerical experiments are performed to show the simplicity and efficiency of the presented method, and all results are performed by using the program Wolfram Mathematica 10.