The evolution of the waves on shallow water surfaces is described by a mathematical model
given by nonlinear KdV and KdV-Burgers equations. These equations have many other …

In this paper, we develop a Bernstein dual-Petrov–Galerkin method for the numerical
simulation of a two-dimensional fractional diffusion equation. A spectral discretization is …

In the spectral Petrov‐Galerkin methods, the trial and test functions are required to satisfy
particular boundary conditions. By a suitable linear combination of orthogonal polynomials …

In this paper, we develop a numerical resolution of the space-time fractional advection-
dispersion equation. After time discretization, we utilize collocation technique and implement …

In this paper, we present a numerical method for solving fractional integro-differential
equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical …

Anomalous diffusion problems are used to describe the evolution of particle's motion in
crowded environments with many applications, such as modeling the intracellular transport …

In this article, we discuss the validity of the discrete maximum principle for the spectral
method called Bernstein-Dual-Petrov-Galerkin method in case of a uniformly elliptic second …

The present work reports an attempt to show the plausibilility of applying fuzzy transform
method (FTM) to work out an approximate solution for space-time differential of non integer …

The mathematical modeling of the large deflections for the cantilever beams leads to a
nonlinear differential equation with the mixed boundary conditions. Different numerical …

The convolution quadrature can be well described by the Mikusinski operational calculus
using convolution semigroup. We present a numerical method for the anomalous diffusion …