Non-standard Finite Difference Based Numerical Method for Viscous Burgers’ Equation

An implicit tailored finite point method for the Burgers’ equation: leveraging the Cole-Hopf transformation

“…Since its origination, a variety of numerical and analytical methods have been employed to address the one-dimensional Burgers' equation. In the past two decades, progress in finding solutions has been made through various approaches such as finite element method [2], variational approach utilizing temporal discretization [3], leastsquares quadratic B-spline finite element method [4], modified Adomianʼs decomposition method [5], variational iteration method [6], collocation of cubic B-splines over finite elements [7], fourth-order finite difference method [8], modified extended tanh-function method [9], Crank-Nicolson finite difference method [10], fourth-order compact finite difference method [11], cubic B-spline quasi-interpolation method [12], differential transformation method [13], uniform Haar wavelet quasilinearization approach [14], modified cubic B-splines collocation method [15], modified cubic-B-spline differential quadrature method [16], weighted average differential quadrature method [17], hybrid scheme [18], high order splitting methods [19], fifth-order finite volume weighted compact scheme [20], exponential modified cubic B-spline differential quadrature method [21], hybrid trigonometric differential quadrature method [22], polynomial based differential quadrature method [23], hybrid Galerkin approximation exponential Euler method [24], fully implicit finite difference method [25], space-time kernel-based numerical approach [26], time symmetric splitting method [27], unified Mahgoub transform and homotopy perturbation method [28], non-standard finite difference scheme [29], spectral solutions [30], undetermined coefficient method [31], modified quartic hyperbolic B-spline DQM [32], and an hybridized non-standard numerical scheme integrating a compact finite difference approach…”

Analytical Method for Solving Inviscid Burger Equation

“…Aswin et al [3] calculated the solution of the viscous BE by using differential quadrature method (DQM). Vijitha et al [27] solved the viscous by novel numerical method and the non-standard finite difference method [14] used to solve the viscous BE and nonlinear PDEs applied to explain the phenomena in the field of mechanics, physics, and biology. Numerous PDEs applied in the field of engineering, fluid mechanics, plasma physics, and chemical physics.…”