Application of Differential Transform Method to the Generalized Burgers–Huxley Equation

In this paper, the differential transform method (DTM) will be applied to the generalized Burgers-Huxley equation, and some special cases of the equation, say, Huxley equation and Fitzhugh-Nagoma equation. The DTM produces an approximate solution for the equation, with few and easy computations. Numerical comparison between differential transform method, Adomian decomposition method and Variational iteration method for Burgers-Huxley, Huxley equation and Fitzhugh-Nagoma equation reveal that differential transform method is simple, accurate and efficient

Finding Exact Solution For Generalized Burgers-Huxley Equation With Constant Coefficients by the modified (G'/G ) expansion method.

  The aim of this work is finding exact solutions to generalized Burger's-Huxley equation with constant coefficients, by using the modified (G'/G )-expansion method, Where we get the application of the steps of the modified (G'/G )-expansion method on the statement of nine equations with nine variables .we solve it with aid of symbolic programs as Maple and Mathematica

Finding Exact Solution For Generalized Burgers-Huxley Equation With Constant Coefficients by the modified (G'/G ) expansion method.

  The aim of this work is finding exact solutions to generalized Burger's-Huxley equation with constant coefficients, by using the modified (G'/G )-expansion method, Where we get the application of the steps of the modified (G'/G )-expansion method on the statement of nine equations with nine variables .we solve it with aid of symbolic programs as Maple and Mathematica

Combined variational iteration method with chebyshev wavelet for the solution of convection-diffusion-reaction problem

The goal of the work is to solve the nonlinear convection-diffusion-reaction problem using the variational iteration method with the combination of the Chebyshev wavelet. This work developed a hybrid iterative technique named as Variational iteration method with the Chebyshev wavelet for the solutions of nonlinear convection-diffusion-reaction problems. The aim of applying the derived algorithm is to achieve fast convergence. During the solution of the given problem, the restricted variations will be mathematically justified. The effects of the scaling and other parameters like diffusion parameter, convection parameter, and reaction parameter on the solution are also focused on by their suitable selection. The approximate results include the error profiles and the simulations. The results of variational iteration with the Chebyshev wavelet are compared with variational iteration method, the Modified variational iteration method, and the Variational iteration method with Legendre wavelet. The error profiles allow us to compare the results with well-known existing schemes

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature

Bivariate pseudospectral collocation algorithms for nonlinear partial differential equations.

Doctor of Philosophy in Applied Matheatics. University of KwaZulu-Natal, Pietermaritzburg 2016.Abstract available in PDF file