Numerical solution of two-dimensional integral equations of the first kind by multi-step methods

‎‎‎In this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (۲D-NVIEs) of the first kind‎. ‎Here‎, ‎we convert a ۲D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎We also verify convergence and error analysis of the method‎. ‎At the end‎, we give some illustrative examples to show the efficiency and accuracy of the presented method.

Keywords:

Two-dimensional nonlinear Volterra integral equations‎ , ‎Integral equations of the first kind‎ , ‎Multi-step methods