The College of Education for Pure Sciences in the Department of Mathematics at the University of Basra discussed a thesis about the Petrov method as the spectral corner of all integral equations
The letter presented by the researcher (Ali Kazem Manati) included
Integral equations appear in physics, engineering, elasticity theory, and mathematical problems for radial heat transformations and radial equilibrium.
The thesis dealt with focusing our attention mainly on finding numerical solutions for several types of integrative equations. The numerical treatment of this type of equations focused on the application of the Petrov Kalrkn spectral method to solve different types of integral equations, where Laguerre polynomials were used as basic functions and Chebyshev polynomials with their weight function as test functions where the integral equations are transformed into a system of algebraic equations that must be solved to get Approximate solutions of these integral equations. The numerical results we obtained showed a great degree of efficiency and good accuracy by applying them to solve seven examples of different types of integrative equations. Moreover, we found that the numerical results obtained from applying SPGM using Laguerre and Chebyshev polynomials are better than the numerical results obtained from applying SPGM using other polynomials, also in the theoretical concept we studied convergence analysis and error analysis