A Novel Numerical Method to Solve the Generalized Burgers-Huxley Equation

This study introduces a computational method to solve the generalized Burgers-Huxley equation which is an equation describing how diffusion, convection, and reaction work in nonlinear wave phenomena. The proposed method involves the exponential B-spline basis function along with the differential quadrature method. The method has good efficiency and accurately presents the behavior of the nonlinear partial differential equations. Ten cases are tested to demonstrate the accuracy of the numerical solution with the exact solutions supported by consistently small L2 and L∞ error. The results show that the method works well and can be applied to solve similar time-dependent nonlinear equations. The present scheme can be further implemented to the higher-dimensional partial differential equations to ensure the efficiency of the scheme in handling the non-linear equations.