ANALYSIS OF A NUMERICAL ALGORITHM FOR THE DIRECT HYPERBOLIC PROBLEM OF NERVE FIBER ACTION POTENTIAL PROPAGATION

Abstract

The subject of research in this work is the direct hyperbolic problem of potential propagation in nerve fibers. The purpose of the study is to analyze the numerical algorithm of the direct hyperbolic problem of potential distribution in nerve fibers.  The analysis of the numerical solution of the direct problem of action potential propagation along a nerve fiber is an important area of research in neurophysiology. Nerve fibers serve as the main channel for transmitting electrical signals in the nervous system, and understanding the process of spreading the action potential through them is of great importance for understanding the mechanisms of nervous transmission and the functioning of the nervous system as a whole. The numerical solution of the direct problem of propagation of the action potential along a nerve fiber consists in numerical modeling of the propagation process and analysis of the results obtained. This approach allows us to investigate various aspects of the propagation process. This article discusses the construction of an algorithm for an approximate solution of the direct problem of hyperbolic type propagation of the action potential of a nerve fiber. The given problem with data on characteristics was solved by the finite-difference method. The stability of the direct problem was established, a solution algorithm was constructed, and a computer implementation was carried out. Graphs of approximate solutions are presented and absolute errors are established, and they are also analyzed by the numerical stability of the algorithm, by variants of model functions, by increasing the parameters of the equation and by the length of the nerve fiber.