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Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this technique have been compared with the exact solution to show the required accuracy of it. Since the scheme is explicit, linearization is not needed and the approximate solution to the nonlinear equation is obtained easily. The effectiveness of this method is verified through illustrative examples. The present method is seen to be a very reliable alternative method to some existing techniques for such realistic problems.

In this article, up to tenth-order finite difference schemes are proposed to solve the generalized BurgersHuxley equation. The schemes based on high-order differences are presented using Taylor series expansion. To establish the numerical solutions of the corresponding equation, the high-order schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the high-order accuracy of the current algorithms with relatively minimal computational effort. The results showed that use of the present approaches in the simulation is very applicable for the solution of the generalized Burgers-Huxley equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithms are seen to be very good alternatives to existing approaches for such physical applications.

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