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

The Volterra-Fredholm Integral Equations (V-FIE) stems from parabolic boundary value issues for an independent random. The linear and nonlinear integral equation has been solved by several scholars. In this paper, the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (VFIE) are presented as an approximate solution, which is deduced using a new approach (Laplace combined homotopy perturbation method (LHPM)). The V-FIE with the Cauchy kernel is considered here. Resolved examples show that the solution proposed is strong, productive and very simple. An interesting aspect of this strategy is that the mistake is too small and it is possible to perform all the calculations quickly. It can be concluded that LHPM is a technique that is very quick, efficient and effective.

**Author(s) Details**

**Dr. Fatheah Ahmed Hendi
**Department of Mathematics, Faculty of Science, King Abdul Aziz University, Jeddah, KSA.

**Department of Mathematics, Faculty of Science, King Khalid University, Abha, KSA.**

Manal Mohamed Al-Qarni

Manal Mohamed Al-Qarni

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/307

Cauchy kernel. Homotopy Perturbation Method (HPM) linear and nonlinear V-FIE Singular integral equation