The College of Education for Pure Sciences, Department of Mathematics, discussed a master's thesis on (Numerical solutions of two-dimensional integral equations using the Petrov-Galerkin spectral method). The thesis presented by the researcher (Shahd Talib Hassan) included:
Integral equations have appeared in many different fields such as engineering, physics and medicine.
The main topic of this thesis focused on numerical solutions of different types of two-dimensional integral equations.
The Petrov-Galerkin spectral method was used with Laguerre polynomials as base functions and Chebyshev polynomials as test functions with their own weight function, where these equations were transformed into a system of linear algebraic equations and solved to obtain numerical solutions, which showed high accuracy and efficiency through its application to nine examples. The aim of the thesis
Finding numerical solutions for linear and nonlinear two-dimensional integral equations using the Petrov-Galerkin spectral method and depending on Laguerre polynomials as base functions and Chebyshev polynomials as test functions with their own weight function.
