In the paper, a newly developed three-point fourth-order compact operator is utilized to
construct an efficient compact finite difference scheme for the Benjamin–Bona–Mahony …

In this paper, we introduce a new finite class of non-polynomial basis functions for the
spectral tau approximation of time-fractional partial differential equations on a semi-infinite …

The aim of this work is to propose two efficient schemes to handle the accuracy near the
singularity at t= 0 in solving two-dimensional time-fractional diffusion-wave equation …

This paper investigates the dynamics of exact travelling-wave solutions for nonlinear spatial
and temporal fractional partial differential equations with conformable order derivatives …

In the Galerkin weak form technique based on various kernels that they do not have δ-
Kronecker property, in order to apply the essential boundary condition, there are two straight …

In this paper, a temporal nonuniform $ L1 $ type difference scheme is built up for the time
fractional diffusion-wave equation with the help of the order reduction technique. The …

The modified second-grade fluid flow across a plate of semi-infinite extent, which is initiated
by the plate's movement, is considered herein. The relaxation parameters and fractional …

In this paper, we extend the application of the hybridized discontinuous Galerkin (HDG)
method to solve time-fractional telegraph equations. In fact, we use an HDG method for …

This paper introduces a new numerical method for solving space-fractional partial
differential equations (PDEs) on non-uniform adaptive finite difference meshes, considering …

In this paper, a new orthogonal system of nonpolynomial basis functions is introduced and
used to solve a class of time-fractional partial differential equations that have nonsmooth …