An implicit fourth-order compact finite difference scheme for one-dimensional Burgers’ equation

A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions

“…In the last decades, there have been great advances in developing high-order compact finite difference schemes for solving partial differential equations and a great deal of research work has been reported [2,4,[6][7][8][9][10][13][14][15]18,19]. Most existing high-order compact schemes are constructed for problems with Dirichlet boundary conditions [6,14] because Dirichlet boundary conditions are simple and straightforward to implement in a high-order compact stencil.…”

An Exponential Finite Difference Method Based on Padé Approximation

“…Gülsu used restrictive Padé approximation classical implicit finite difference method for the Burgers' equation [15]. Liao applied a fourth-order compact finite difference method to the equation [16]. Sari and Gürarslan defined a sixth-order compact finite difference method for numerical solution of the onedimensional Burgers' equation [17].…”

Construction of Compact Finite Difference Schemes by Classic Differential Quadrature

“…Usually, the compact schemes have much smaller numerical dispersion and dissipation errors than traditional finite difference schemes of the same order of accuracy on the same mesh. So far, researchers have developed a variety of compact difference schemes [2][3][4][5][6].…”