A robust Hermite spline collocation technique to study generalized Burgers-Huxley equation, generalized Burgers-Fisher equation and Modified Burgers’ equation

• The proposed technique is very simple, fast, easy to implement but very efficient. • The technique solves the nonlinear partial differential equations directly without transforming them into heat equation or ordinary differential equations. • The technique does not require unnecessary integration or calculation of weight functions as the case of other numerical methods for instance Galerkin methods, spectral methods etc. • The technique does not require much computation effort. Due to the use of Hermite splines, the easily solvable banded system of algebraic equations is obtained. • The efficiency and robustness of the technique are shown by numerically solving five examples of these three non-linear partial differential equations for different parameters. In this paper, a robust Hermite collocation technique is proposed to find the numerical solution of generalized Burgers-Huxley and Burgers-Fisher equations as well as modified Burgers’ equation. In this technique, Hermite collocation method with fifth order Hermite splines have been used to approximate the solution variable and its spatial derivatives. Crank-Nicolson finite difference scheme is applied on time derivatives. The quasilinearization technique is used to linearize the nonlinear terms in the equation. Von-Neumann method is applied to show stability of the proposed technique. Robustness of proposed technique is shown by solving five test examples of these three equations with different parameters. The computed numerical results are better than the results from other techniques compared in this paper and are also matched well with the exact solutions.