Solving Burger-Fisher Equation (BFE) by using Banach Contraction Method (BCM) / Fateen Nuraribah Ahmad Fadhli, Nurul Izzah Zahra Shahrulanuar and Saidahtul Izyan Izzati Mohamad Sazali - Ahmad Fadhli, Fateen Nuraribah; Shahrulanuar, Nurul Izzah Zahra; Mohamad Sazali, Saidahtul Izyan Izzati (2023)
In this article, we propose a method for solving the Burger-Fisher equation. The proposed method is the Banach Contraction Method (BCM). The Burger-Fisher equation is a combination of the Burger equation and the Fisher equation. There have been many methods used to solve the problem associated with the Burger-Fisher Equation, such as the Adomian Decomposition Method (ADM) and the Local Discontinuous Galerkin (LDG) method. However, the computations of these methods use too much computer memory because the data to be processed is large. Therefore, this paper presents the results of the research findings with two main objectives: We used the BCM to solve the Burger-Fisher Equation, followed by validating the accuracy of the BCM with the exact solutions. Plus, in this study, calculations were mainly performed using the MAPLE 2018 software to facilitate the calculations and simplify the complicated results. As for the scope of this study, we cover the partial differential equation specifically in terms of the Burger-Fisher Equation and the BCM. In summary, the method used in this study has introduced a straightforward mathematical method for solving various differential equations, which improves and expands our knowledge in the field of mathematics. Currently, all the articles related to Burger-Fisher Equation and BCM are applicable in this study. Also, a procedure for implementing the method is provided, along with an error analysis.