Recent Advancements: Numerical Solution of Nonlinear Mixed Integral Equation with a Generalized Cauchy Kernel

The Volterra-Fredholm integral equations (V-FIE) arises from parabolic boundary value problems. Many
authors have interested in solving the linear and nonlinear integral equation. In this article, we present
approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (VFIE),
which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)).
Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is
powerful, effective and very simple. An interesting feature of this method is that the error is too small and all the
calculations can be done straightforward. It can be concluded that LHPM is a very simple, powerful and
effective method.