Matrix Algorithms Based on Jacobi and Romanovski-Jacobi Polynomials for Solving the FitzHugh-Nagumo Nonlinear Equation

Abstract

The present paper develops and makes efficient, a new, state-of-theart numerical technique for solving the FitzHugh-Nagumo Nonlinear Equation (FH-NNE) with initial and boundary conditions, which represents perhaps the simplest mathematical model for discussing biological systems, including nerve signals and cardiac behavior. Which consists of operational matrices and spectral techniques based on Jacobi and Romanovski-Jacobi polynomials. It is ensured that the nonlinear system is modeled so accurately that it can be effectively solved to ensure the best accuracy combined with computational economy. Comparing the results with the respective numerical results, it is seen that the proposed techniques outdo the standard ones as respects accuracy and efficiency of computation.OPEN ACCESS Received: 11/01/2025 Accepted: 25/02/2025 Published: 07/04/2025

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