Numerical simulation of soliton solutions of nonlinear Fitzhugh-Nagumo equation by using LOOCV with exponential B-spline with Significant Applications in Neurosciences

This study focuses on solving the one-dimensional nonlinear Fitzhugh-Nagumo (FHN) equation using a novel technique called the “Exponential modified cubic B-spline differential quadrature method” combined with “leave-one-out cross-validation”. The inclusion of leave-one-out cross-validation (LOOCV) is essential for finding the optimal value of the parameter \(\:\lambda\:\), which is a key component in the exponential modified cubic B-spline basis functions, thereby enhancing the accuracy and robustness of the results. By incorporating this unique combination of LOOCV and the exponential modified cubic B-spline differential quadrature method, the research introduces a new computational approach that could be of considerable interest to scholars in the field. This method has been applied to four different examples of the Fitzhugh-Nagumo equation, with outcomes detailed in tables and figures. This paper presents the methodology and results of a study on the equation, emphasizing its significance and applications in neuroscience. The Fitzhugh-Nagumo model is highlighted as a versatile tool across various scientific, engineering, and mathematical fields, with a particular focus on its role in understanding the complex dynamics of neural systems and its potential impact on future research and real-world problems.