Within the numerical framework of non-homogeneous Riemann solver (NHRS) the
nonlinear models characterizing traffic flows are investigated. Namely, we investigate the …

In this paper, we consider three models of non-linear Schrödinger's equations (NLSEs) via It
o sense. Specifically, we study these equations forced by multiplicative noise via the …

This paper presents numerical modeling and investigation for the Ripa system. This model is
derived from a shallow water model by merging the horizontal temperature gradients. We …

We propose a class of finite volume algorithms that are both simple and efficient for solving
numerically the shallow water equations with varying densities; shallow water flows in single …

We introduce some vital solutions for the dusty gas flow. Specifically, we implement the
nonhomogeneous Riemann solver (NHRS) scheme in order to investigate the unsteady …

In the current paper, we develop and suggest a modified Rusanov method for simulating two-
layer shallow water flows with variable topography. The coupling between two-layers results …

In this work, we consider the model of shallow water equation with horizontal density
gradients. We develop the modified Rusanov (mR) scheme to solve this model in one and …

The Brio system is a nonlinear system of conservation laws that is used to analyze plasmas.
The current research presents numerical solutions to this model exposed to initial conditions …

We investigate the conservation laws that explain the chemistry process of isolating a single
component from a mixture using column chromatography. We construct the modified …

The shear shallow water (SSW) model introduces an approximation for shallow water flows
by including the effect of vertical shear in the system. Six non-linear hyperbolic partial …