A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning

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

“…-has given marginally more accurate results to those in [16] for all time levels and  ,  used, -for fixed  ,  and •  , the accuracy increases and U tends to identify with u at long time level as  is refined, •  , as  increases, the accuracy decreases.…”

“…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. Batiha et al [17] used the variational iteration method and Khattak [18] the collocation method with radial basis functions.…”

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

“…Several numerical techniques have been developed to find the numerical solution of GBF and GBH equations. Javidi presented the numerical solution of GBH equation using spectral collocation method [20] and pseudospectral and preconditioning [21] and Chebyshev polynomials to develop a new domain decomposition algorithm [22]. Golbabai and Javidi [23] applied a spectral domain decomposition technique for the numerical solution of GBF 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. The results of the proposed method in terms of errors comparative to Local Radial Basis Function Differential Collocation method (LRBFDQ) [58] is provided in Table 5.…”

Application of spectral collocation method to a class of nonlinear PDEs

“…3) where δ , β ≥ 0 and γ ∈ (0, 1) are given parameters, IV) generalized Burger's-Huxley equation [7,8] 4) with equation (2.7), we obtain the fundamental recurrence relation T n (x) = 2xT n−1 (x) − T n−2 (x), n = 2, 3, . .…”