The College of Education for Pure Sciences, Department of Mathematics, organized a scientific lecture entitled (Integrating the least squares method with the Togard polynomial to solve mixed differential-integral equations)
The lecture presented by the lecturer (Zahraa Adnan Jameel) included:
This episode dealt with the use of the well-known least squares method (LSM) combined with Tugard polynomials (TPs) of different degrees to find numerical solutions to the Volterra-Friedholm differential-integral equations (VFIDEs) and the Volterra-Friedholm mixed integral-differential equations (MIDEs) of the second kind, where there are Many methods have found the approximate solution to differential-integral equations, such as the Adomian analysis method, the modified Adomian analysis method, the homotopic analysis method...etc. As the method is based on combining both the least squares method and Togard polynomials, a system of algebraic equations is generated that can be solved using previously known methods for solving linear systems. A number of examples were solved to demonstrate the accuracy and effectiveness of the presented method with a relatively small number of iterations. When the results of the current method are compared with the results of other methods, the approximate results obtained by the proposed method confirm its accuracy and efficiency. The applicability of the proposed method was also proven and convergence analysis was discussed.
