Optimal Perturbation Iteration Method for Bratu-Type Problems
This work offers an improved numerical method for solving nonlinear differential equations, which is relevant for researchers in applied mathematics and engineering.
The paper proposes an optimal perturbation iteration method for solving nonlinear differential equations, specifically Bratu-type problems, achieving more accurate and efficient approximate solutions with fewer terms compared to existing methods.
In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature.