Abstract A quasi–second-order scheme is developed to obtain approximate solutions of the two-dimensional shallow water equations (SWEs) with bathymetry. The based on a staggered finite volume space discretization: scalar unknowns are located in discretization cells while vector edges mesh. monotonic upwind-central for conservation laws (MUSCL)-like interpolation discrete convection operators he...

Based on the recent development of Jacobian-free Lax–Wendroff (LW) approaches for solving hyperbolic conservation laws (Zorio et al. in J Sci Comput 71:246–273, 2017, Carrillo and Parés 80:1832–1866, 2019), a novel collection explicit multistage multiderivative solvers is presented this work. In contrast to Taylor time-integration methods, Runge–Kutta (MDRK) techniques achieve higher-order cons...

The objective of this problem is to study ant foraging lines in one and two dimensions in order to understand their dynamics and examine the fitness of ant colonies. A simple model to describe ant traffic is formulated using conservation laws and a behavioral model. In this work, the behavioral model assumes that the concentration of pheromones is simply proportional to the density of ants. Thi...

the dynamics of multicomponent adsorption in a fixed bed adsorber is examined numerically. the dynamic model of adsorption in the packed column included axial dispersion and variable space velocity along the bed for the multicomponent adsorption adsorption the pore fluid and the solid phase are in equilibrium with a nonlinear isotherm. the numerical solution is based upon the modified lax-wendr...

In everyday life human faces shock waves and rarefaction largely in their surroundings. Hence it’s necessary to know the behavior of these protect destructive effects. The aim this work observe propagation various dynamics due solve non-linear hyperbolic inviscid Burgers’ equation numerically. models adopted here two numerical schemes which enable us first order explicit upwind scheme (EUDS) se...