The College of Education for Pure Sciences at the University of Basrah  discussed a PhD thesis on a mathematical method to solve some non-linear problems
The thesis presented by the researcher (Jihad Muhammad Kazem) included
       In this thesis, a new computational method called functions of the fourth degree hat (FDHFs) is introduced using fourth degree polynomials to solve many nonlinear problems. In fact, the idea of constructing FDHFs is inspired by general hat functions (GHFs), modified hat functions (MHFs), and adjustment hat functions (AHFs), which are constructed using polynomials of first, second, and third degree, respectively. There are two main steps in the proposed method. The first is to focus on using FDHFs to transform the problem under study into a system of nonlinear algebraic equations. While the second step focuses on solving the system of nonlinear algebraic equations numerically.
This method has been used to solve many nonlinear problems, including Volterra's integral equations, integral differential equations, fractional integral differential equations, stochastic differential equations, fractional stochastic differential equations, optimal control problems, and fractional optimal control problems. To prove the accuracy of the proposed method and its applicability, many examples of the issues studied in this thesis were studied, and we made a comparison between the proposed method and its counterparts of hat functions (GHFs, MHFs, and AHFs), and it was found that the results obtained using our proposed method are better than those obtained Obtained using other hat function methods in terms of accuracy and speed of implementation.