Numerical Study of Fractional Order Burgers’-Huxley Equation Using Modified Cubic Splines Approximation

This paper aims to explore the numerical solution of non-linear fractional-order Burgers’-Huxley equation based on Caputo’s formulation of fractional derivatives. The equation serves as a versatile tool for analyzing a wide range of physical, biological, and engineering systems, facilitating valuable insights into nonlinear dynamic phenomena. The fractional operator provides a comprehensive mathematical framework that effectively captures the non-locality, hereditary characteristics, and memory effects of various complex systems. The approximation of temporal differential operator is carried out through finite difference based L1 scheme, while spatial discretization is performed using modified cubic B-spline basis functions. The stability as well as convergence analysis of the approach are also presented. Additionally, some numerical test experiments are conducted to evaluate the computational efficiency of a modified fourth-order cubic B-spline (M43BS) approach. Finally, the results presented in the form of tables and graphs highlight the applicability and robustness of M43BS technique in solving fractional-order differential equations. The proposed methodology is preferred for its flexible nature, high accuracy, ease of implementation and the fact that it does not require unnecessary integration of weight functions, unlike other numerical methods such as Galerkin and spectral methods.