Numerical integration of differential equations, as an essential tool for investigating the
qualitative behaviour of the physical universe, is a very active research area since large …

In this manuscript, we consider an initial-boundary-value problem governed by a (1+ 1)-
dimensional hyperbolic partial differential equation with constant damping that generalizes …

In this work, we investigate numerically a nonlinear hyperbolic partial differential equation
with space fractional derivatives of the Riesz type. The model under consideration …

In this paper, based on the theory of rooted trees and B-series, we propose the concrete
formulas of the substitution law for the trees of order= 5. With the help of the new substitution …

In this paper we propose and investigate a general approach to constructing local energy-
preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian …

In this paper we study the geometric numerical solution of the so called “good” Boussinesq
equation. This goal is achieved by using a convenient space semi‐discretization, able to …

Two energy-preserving schemes are proposed for the “good” Boussinesq (GBq) equation
using the Hamiltonian Boundary Value and Fourier pseudospectral methods. The equation …

For many practical actuators, laws of motion quantities are directly imposed to control the
motion of mechanical systems. Motivated by this point, considering motion quantities as …

In this work, a three-level implicit compact difference scheme for the generalised form of
fourth order parabolic partial differential equation is developed. The discretization is derived …

We propose a Deuflhard-type exponential integrator Fourier pseudo-spectral (DEI-FP)
method for solving the “Good” Boussinesq (GB) equation. The numerical scheme is based …