Error analysis and numerical solution of Burgers–Huxley equation using 3-scale Haar wavelets

Two-Dimensional Uniform and Non-Uniform Haar Wavelet Collocation Approach for a Class of Nonlinear PDEs

“…The uniform Haar wavelet was suggested by Celik et al [53] to study various applications of the generalized B-H equation. Shukla and Kumar [54] used a combination of the uniform Haar wavelet analysis and the Crank-Nicolson finite difference approach to numerically solve the B-H problem. Recently, Verma et al [55] developed a numerical technique based on the uniform Haar wavelet and non-standard finite difference scheme for solving a class of extended Burgers equations.…”

Numerical Approximation of Generalized Burger’s-Fisher and Generalized Burger’s-Huxley Equation by Compact Finite Difference Method

“…Recently, the exact solution has been computed by Kushner and Matviichuk [39] using the theory of finitedimensional dynamics. Shukla and Kumar [40] applied the numerical scheme based on the Crank-Nicolson finite difference method in collaboration with the Haar wavelet analysis, to obtain the numerical solution. A feed-forward artificial neural network technique is applied by Panghal and Kumar [41] in which the constructed error function is minimized using the quasi-Newton algorithm.…”

Conforming, nonconforming and DG methods for the stationary generalized Burgers- Huxley equation

“…The recent literature relevant to the construction and analysis of discretizations for (1.1) and closely related problems is very diverse. For instance, numerical methods specifically designed to capture boundary layers in singularly perturbed generalized Burgers-Huxley equations have been studied in [18], different types of finite differences have been used in [23,19,25,28], spectral, B-spline and Chebyshev wavelet collocation methods have been advanced in [1,15,31,7], numerical solutions obtained with the so-called adomain decomposition were analyzed in [14], homotopy perturbation techniques were used in [20], Strang splittings were proposed in [8], meshless radial basis functions were studied in [17], generalized finite differences and finite volume schemes have been analyzed in [9,33] for the restriction of (1.1) to the diffusive Nagumo (or bistable) model, and a finite element method satisfying a discrete maximum principle was introduced in [12] (the latter reference is closer to the present study). Although there is a growing interest in developing numerical techniques for the generalized Burgers-Huxley equation, it appears that the aspects of error analysis for finite element discretizations have not been yet thoroughly addressed.…”