A flow field over a rigid wavy surface is numerically generated. The general concept of the large eddy simulation that captures the large scale flow structure is utilized. A coordinate transformation scheme is developed to transform any wavy surface to a flat surface. The numerical computations are carried out in the co ~ domain. The subgrid scales are resolved by utilizing a Smagorinsky subgri...

In this paper, the (m+1)-step Adams-Bashforth, Adams-Moulton, and Predictor-Correctormethods are used to solve rst-order linear fuzzy ordinary dierential equations. The conceptsof fuzzy interpolation and generalised strongly dierentiability are used, to obtaingeneral algorithms. Each of these algorithms has advantages over current methods. Moreover,for each algorithm a convergence formula can b...

In this study, we propose new illustrative and effective modeling to point out the behaviors of Hepatitis-B virus (Hepatitis-B). Not only do consider mathematical modeling, equilibria, stabilities, existence–uniqueness analysis model, but also, make numerical simulations by using Adams–Bashforth scheme. However, apply parameter estimation method determine our model parameters find curve that be...

This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods. These methods are aimed at solving conservation laws and allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL co...

In this chapter, some real-life model problems that can be formulated as ordinary differential equations (ODEs) are introduced and numerically studied. These models are the variable-order fractional Hodgkin–Huxley model of neuronal excitation (VOFHHM) and other models with the variable-order fractional (VOF) time delay, such as the 4year life cycle of a population of lemmings model, the enzyme ...

Assuming that the population remains small, one can truncate at given values of n1 and n2 to yield a finite set of differential equations. For an initial condition, we take the population to be zero, that is, ρ1,1,1,1 = 1 with all other elements of the density matrix set to zero. Eq. A.6 can then be solved numerically (we used the Adams-Moulton-Bashforth procedure) until a steady state is reach...

The classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope (e.g., specialized recursions for centered and staggered approximations, for Adams–Bashforth-, Adams–Moulton-, and BDF-formulas for ODEs, etc.). Two recent algorithms overcome these problems. For equispaced grids, such weights can be found very convenien...

The basic ideas of semi-implicit time differencing are reviewed, including analytical results not widely referenced in the meteorological literature. It is shown that solving the resulting implicit equations by simple fixed-point iteration requires a relatively small time step to guarantee convergence, thus defeating the purpose of the semiimplicit method. In contrast, classical iteration metho...