Two approximated techniques for solving of system of two-dimensional partial integral differential equations with weakly singular kernels

In this work, two approximation technique is presented for the solution of system of two-dimensional nonlinear Volterra-Fredholm partial integral differential equations with weakly singular kernel using Hermite wavelets and Gegenbauer wavelets. For this purpose, the operational matrices are introduced. By solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the two methods. In addition, by means of error analysis and some numerical results, the accuracy and efficiency of the methods are scrutinized and interpreted.