Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation

Abstract

Numerical treatments for the generalized Burger's—Huxley GBH equation are presented. The treatments are based on cardinal Chebyshev and Legendre basis functions with Galerkin method. Gauss quadrature formula and El-gendi method are used to convert the problem into a system of ordinary differential equations. The numerical results are compared with the literatures to show efficiency of the proposed methods.

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

“…Celik [43] proposed a Chebyshev wavelet collocation method based on truncated Chebyshev wavelet series for the solution of GBH equation. Moreover, the numerical solution of proposed GBH equation was obtained using several numerical methods named Galerkin method [44], implicit and fully implicit exponential finite difference methods [45], Haar wavelet method [46], conditionally bounded and symmetrypreserving method [47], linearly implicit compact scheme [48], positive and bounded finite element method [49], explicit solution scheme [50], exponential time differencing scheme [51], and higher order finite difference schemes [52].…”

“…In Table 9, we tabulate a comparison between HBSCM and the existing methods CFDS [26], FONS [33], ADM [38], Galerkin method (GM) [44], higher order finite difference method (HFDM) [52], MCBS [55], cubic B-spline algorithm (CBSA) [56], and optimal homotopy asymptotic method (OHAM) [69] at = 1, 3. Computations of the absolute errors and two different types of error norms have been mentioned in Tables 10 and 11, respectively.…”

Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation

“…However, the spline collocation method for the Burgers-Huxley equation was discussed in a book by Schiesser [12]. In addition, many other analytical and numerical methods for generalized Burgers-Huxley equations have been developed in the past, see for example [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

“…These include optimal homotopy asymptotic method by Ali et al (2012), Adomian decomposition technique by Ismail et al (2004), Haar wavelet method by Celik (2012), computational meshless method by Khattak (2009). Many other techniques can be found in references (Mittal and Tripathi, 2015;Jiwari el al., 2013;El-Kady et al, 2013;Macías-Díaz and Szafrańska, 2014;Ervin et al, 2015).…”