Existence, Uniqueness, and Numerical Solutions for 2D Volterra-Fredholm Equations with Singular Kernels

Mustafa Ali Hussein  Al-Mohammadi

Mustafa Ali Hussein Al-Mohammadi Islamic Azad University, Shiraz Branch, Iran

Keywords: Integral Equations, Volterra-Fredholm, Singular Kernels, Tau Method, Numerical Methods

Abstract

Vaultra-Fredhom Integrated integrated integrated equations and non-linear cores have extensive applications in modelling complex physical problems such as heat transfer, fluid mobility and image processing. Because of their special complications, these equations are difficult to solve analytically and require effective and stable numerical methods to get an accurate solution. The main objective of this research is to investigate the existence and specificity properties of the two-dimensional Volterra peace-to-life solution. In this connection, the taum method was used as an accurate numerical technique to solve both linear and non-linear equations. In this study, integrated equations were converted to algebraic systems, and their numerical solutions were achieved effectively using base functions and a series of appropriate mats. The results suggest that the taum method is able to show high stability in producing accurate solutions for complex equations under different border conditions and solving equations with a cynical core. This research is used especially in engineering and physics in non -linear and complex problems.

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