In this popular text for an Numerical Analysis course, the authors introduce several major
methods of solving various partial differential equations (PDEs) including elliptic, parabolic …

A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-
order compact finite difference method. To achieve this, a tridiagonal sixth-order compact …

In this paper, we present and analyze fully discrete finite difference schemes designed for
solving the initial value problem associated with the fractional Korteweg-de Vries (KdV) …

In this paper, we propose a generalized framework for the derivation of compact difference
schemes for the approximation of an arbitrary order derivative. We formulate a methodology …

The main aim of present work is to develop the two meshless collocation methods based on
radial basis function-generated finite difference (RBF-FD) and global RBF (GRBF) methods …

In this paper we develop a sixth-order compact scheme coupled with Alternating Direction
Implicit (ADI) methods and apply it to parabolic equations in both 2-D and 3-D …

In this study, a high-order compact finite difference method is used to solve boundary value
problems with Robin boundary conditions. The norm is to use a first-order finite difference …

In this article, numerical solutions of the generalized Burgers–Fisher equation are obtained
using a compact finite difference method with minimal computational effort. To verify this, a …

The invariant preserving property is one of the guiding principles for numerical algorithms in
solving wave equations, in order to minimize phase and amplitude errors after long time …

In this paper, we study the stability and convergence of a fully discrete finite difference
scheme for the initial value problem associated with the Korteweg-De Vries (KdV) equation …