The College of Education for Pure Sciences, Department of Mathematics, University of Basrah, organized a scientific lecture entitled (New Numerical Methods for Solving Initial Value Problems Based on Quadratic Integration Formulas)
The lecture presented by the student (Zainab Jawad Kazem) included
In this study, we present several new numerical methods for solving initial value problems (IVPs) based on two quadratic formulas for integration using hybrid functions and Bernstein polynomials with Taylor series expansion. These methods are of the Range-Kota formulas. These methods were found to be stable and of the second and third orders of convergence. We use some initial value problems in the ordinary differential equations to demonstrate the efficiency of these methods. Finally, our new methods are a suitable option for studying IVPs.