A Combined Taylor–Bernstein Approximation for Solving Non-linear Fitz-Hugh–Nagumo Equation

In this paper, a new combined approximation technique is developed to solve the Fitz-Hugh–Nagumo (FHN) equation. This combined technique is based on Taylor’s expansion which discretizes the time derivative and the Bernstein polynomials which are utilized for space derivatives. The FHN equation reduces to a system of linear algebraic equations for each time step via some suitable collocation points. Here, we also suggested the existence and uniqueness of the problem. Convergence analysis of the combined technique is also presented here. To show the applicability and accuracy of the present method, the numerical results are compared with the same by some recent existing methods. Three test problems are solved to demonstrate the effectiveness of the proposed method and are presented in tables and graphics.