Galerkin approximation of Burgers-Huxley equation with fractional order arising in reaction mechanism and diffusion transport

Abstract Burgers-Huxley model depicts a prototype model of the interaction of convection effect, reaction mechanisms and diffusion transport, used to study the liquid crystal and nerve fibers. This study introduces Galerkin approximation for time-fractional Burgers-Huxley equation (TFBHE). The Caputo derivative is used to evaluate the temporal part using the L 1 formula. The Galerkin approach employs cubic B-spline as a shape and test function, resulting in a symmetric matrix that is easily convergent. In addition, the three-point quadrature rule is implemented to evaluate the integration of complex function . The Von Neumann analysis is used to discuss stability of the scheme. The performance and robustness of the technique is measured using various error norms The results are compared with the exact solution, demonstrating effectiveness of the proposed method.