Abstract
This research paper studies the computational and numerical solutions of the transmission of nerve impulses of a nervous system (the neuron) by applying the modified Khater (mK) method and B-spline scheme to the FitzHugh-Nagumo (FN) equation where it is usually used as a model of the transmission of nerve impulses. This study focuses on finding the different types of soliton wave solutions, studying the stability property of them, and then use them to obtain the numerical solutions of the model. The obtained solutions are compared with each other to show the absolute value of error between them that will explain the accuracy of both types of solutions. Moreover, in the text of more explanation of the physical properties of the suggested model, some sketches are plotted. Also, the performance of both techniques is investigated to show its ability for applying to other nonlinear evolutions equation.