Discrete Adomian decomposition method for solving Burger's-Huxley equation

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

“…The approximate solutions were obtained for the GBH and GBF equations using the Adomian and discrete Adomian decomposition methods [40,41]. Inan and Bahadir [42] obtained a numerical solution of the GBH equation using implicit exponential finite difference method.…”

An Efficient Local Formulation for Time–Dependent PDEs

“…We have used the parameters values α = β = δ = 1 and γ = 0.001 and time step length ∆t = 0.0001, spatial domain [−10, 20], N = 61 using IMQ RBF. From Table 3, we have noted that the RK4 produced more accurate results than the results reported in [12,14,15]. 1.0 0.1 8.16 × 10 −11 0.0 × 10 −9 3.88 × 10 −6 3.75 × 10 −7 0.5 4.41 × 10 −11 0.0 × 10 −9 3.88 × 10 −6 3.75 × 10 −7 0.9 6.61 × 10 −12 0.0 × 10 −9 3.88 × 10 −6 3.75 × 10 −7 Table 4 also shows the comparison of numerical results produced by the LMM with the results of Haar wavelet method given in [13].…”

“…Summary of numerical results is given as: Results of 1D fifth order KdV equation are shown in Table 1 and compared with the method in [3] whereas numerical results of seventh order KdV equation are presented in Table 2. Similarly the numerical results of generalized Burgers' Huxley equation are presented in Tables 3 and 4 and the results are compared with the methods given in [12][13][14][15] while the numerical results of Huxley equation are shown in Tables 5 and 6 and compared with the methods in [14,15,19]. Numerical results of generalized Burgers' Fisher equation are shown in Table 7 and compared with the methods in [14,15].…”

“…In Table 3, we have compared the results obtained by the LMM for generalized Burgers' Huxley equation for Test Problem 3 with the methods given in [12,14,15]. We have used the parameters values α = β = δ = 1 and γ = 0.001 and time step length ∆t = 0.0001, spatial domain [−10, 20], N = 61 using IMQ RBF.…”

“…In general it is difficult and sometimes impossible to get exact solution of such type of nonlinear PDEs. Researchers employed different numerical techniques which include discrete Adomian decomposition method [12], Haar wavelet method [13], Adomian decomposition method [14], meshless collocation method based on RBF [15] and local meshless method [16] for the solution of Burgers' Huxley equation. The Huxley model equation [17] describes nerve pulse propagation in nerve fibres and wall motion in liquid crystals [18].…”