The University of Basra discusses a master’s thesis in the College of Education for Pure Sciences entitled (Numerical solutions to mixed differential-complementary equations by integrating the method of least squares with orthogonal polynomials)

The thesis presented by the researcher (Ehsan Fayez Shoshan) included the merging of the least squares method with orthogonal polynomials (Shbishev, Legendre, Euler and Laquiere) to obtain approximate solutions of mixed differential-integral equations, whereby these methods resulted in a linear algebraic system of equations and polynomial coefficients.

The thesis concluded the numerical results resulting from solving these algebraic systems on the efficiency and accuracy of the proposed methods, by applying them to seven examples for the purpose of finding approximate solutions that were compared with the analytical solutions. From the rest of the methods, and then we discussed a convergence analysis of all the methods proposed in this thesis