Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit finite difference methods

Du Fort–Frankel finite difference scheme for Burgers equation

“…In Table 3 Table 14 we compare our results with results of Kutluay et al [5] for ν d = 0.02, h = 0.0125 and k = 0.0001. This comparison shows that Du Fort-Frankel is giving good results.…”

“…It can also be used to test the various numerical algorithm. Due to its wide range of applicability, researchers [3,5,7] were attracted to it and studied properties of its solution using various numerical techniques.…”

“…In [5] using the Hopf-Cole transformation the Burgers equation is reduced into linear heat equation and a standard explicit finite difference approximation is derived. Then assuming that this explicit finite difference scheme has product solution, they derived exact explicit finite difference solution which converges to the Fourier solution as mesh size tends to zero.…”

A New Time Stepping Method for Solving One Dimensional Burgers' Equations

“…These aims will be done by comparing ECEM to other numerical approaches based on the finite difference method [16,23], finite element method [28], cubic spline and sinc-function methods [31,32], and the fourth-order Runge-Kutta method [21] (RK4) and the BDF-type Chebyshev approximation based fourth-order implicit Runge-Kutta method [29] (CCM). The numerical errors are measured by the following maximum and l 2 norms…”

“…For example, one may refer to the approaches based on the finite difference method ( [2,12,16,18,20,23,27]), Galerkin method ( [11,17,33]), finite element method ( [1,8,10,19,24,28]), spectral method ( [4,6,26]) and cubic spline and sinc-function methods ( [1,24,31,32] etc. Most of the mentioned numerical approaches are using various computational techniques in spatial discretizations to get more accurate approximations.…”