A parameter-uniform implicit difference scheme for solving time-dependent Burgers’ equations

On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems

“…Singularly perturbed partial differential equations relate an unknown function to its derivatives evaluated at the same instance. We can see these types of problems in [32][33][34][35][36][37][38]. Singularly perturbed partial differential equations have been studied extensively by many authors and developed thoroughly over the recent decades [29,30].…”

“…But, when the delay is of big order of the singular perturbation parameter, the use of Taylor's series expansion for the term containing delay may lead to a bad approximation. We can see these types of problems in [32][33][34][35][36][37][38]. In this article, we suppose that r > 0 the delay parameter is big and proposes a special method for discretization of continuous time-delay.…”

Contemporary review of techniques for the solution of nonlinear Burgers equation

“…To handle the non-linearity of Burgers equation, [80] used quasilinearzation process, where a standard implicit finite difference scheme is employed, to discretize temporal domain and a standard upwind finite difference scheme, to discretize in spacial direction on piecewise uniform mesh. Choosing Multiquadric (MQ) as a spatial approximation scheme, Hon et al [81] presented a different scheme, where a low order explicit finite difference approximation of the time derivative is employed for the sake of comparison.…”

Multilevel augmentation methods for solving the Burgers' equation

“…In 1972, Benton and Platzman published a number of distinct solutions to the initial value problems for the Burgers equation in the infinite domain as well as in the finite domain. Numerical solutions of the Burgers' equation were studied extensively in the literature . Specifically, readers can refer to for finite difference methods, for finite element methods, for spectral methods, for splitting‐up methods, and so forth.…”