A Modified Collocation Technique for Addressing the Time-Fractional FitzHugh–Nagumo Differential Equation with Shifted Legendre Polynomials

This study is devoted to solving the nonlinear inhomogeneous time-fractional FitzHugh–Nagumo differential problem (TFFNDP) using the spectral modified collocation method. The proposed algorithm uses non-symmetric polynomials, namely shifted Legendre polynomials (SLPs), which are orthogonal. The orthogonality property of SLPs and certain relations facilitate the acquisition of accurate spectral approximations. Comprehensive convergence and error studies are conducted to validate the accuracy of the suggested shifted Legendre expansion. Several numerical examples are presented to demonstrate the method’s effectiveness and accuracy. The proposed scheme is benchmarked against known analytical solutions and compared with other algorithms to ensure the applicability and efficiency of the proposed algorithm.