Solving the generalized Burgers–Huxley equation using the Adomian decomposition method

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

“…Morufu [37] developed an improved algorithm for solving GBF equation based on a Maple code. Hashim et al [38] applied Adomian decomposition method (ADM) to get rapidly convergent analytical series solution of the GBH equation.…”

“…Table 2 shows a comparison of the absolute errors at = 3.9, = 1, 2, 3 obtained by proposed method HBSCM with the methods existing in the literature named compact finite difference scheme (CFDS) [26], a fourth-order improved numerical scheme (FONS) [33], variational iteration method (VIM) [36], Adomian decomposition method (ADM) [38,40], implicit exponential finite difference method (IEFM) [42], and modified cubic B-spline (MCBS) [55]. The obtained results are compared with Haar wavelet method (HWM) [46] at = 0.8 in Table 3 while a comparison between HBSCM and a new domain decomposition method (NDDA) [22] can be observed in Table 4.…”

“…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.…”

A Fourth Order Improved Numerical Scheme for the Generalized Burgers—Huxley Equation

“…A theoretical study of the BgH equation was found in Wang et al [4], while analytical solutions using various techniques in [7][8][9][10][11], etc., have been proposed. As far as the numerical methods are concerned among others the Adomian decomposition method was used by Ismail et al [12] for the BgH and the Burgers-Fisher equation, and by Hashim et al [13] for the BgH equation. Javidi [14] used the pseudospectral method, while Javidi [15], Javidi and Golbabai [16] the spectral collocation method.…”

Highly Accurate Scheme for the Cauchy Problem of the Generalized Burgers-Huxley Equation

“…The generalized Burgers-Huxley equation has been considered recently by researchers that developed some analytical and numerical methods for its solution. Schemes such as the adomian decomposition [14], homotopy perturbation [15], homotopy analysis [16], and reduced differential transform [17] were proposed to solve the initial value problem of the Burgers-Huxley equation. Moreover, some authors considered the initial boundary value problem of this equation and used spectral collocation [18], finite-difference [19,20], Haar wavelet [21] and modified cubic B-spline differential quadrature [22] methods for its solution.…”