Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, to be consistent with the physical problem, a parameter ? presented. The boundedness, existence, and positivity solutions for proposed are discussed. Two improved numerical methods presented Caputo proportional constant nonstandard modified Euler–Maruyama met...

Abstract We propose a new theory based on the notions of marginal and large difference which has natural models in context nonstandard mathematics. introduce notion finite marginality show representation result ensures, for finitely countable models, existence homomorphism structure into model numbers, extent to any such is unique. Finally, we that our constitutes part underlying abstract three...

The stability and convergence properties of the mimetic finite difference method for diffusion-type problems on polyhedral meshes are analyzed. The optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved.

The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed model ordinary differential equations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. F...

It is important to simulate a groundwater transport process, e.g., pollutant migration, through the vadose zone and subsequent mixing within the saturated zone to assess potential impacts of contaminants in the subsurface in preliminary stages. It is challenging to simulate heterogeneous soil characteristics and non-uniform initial contaminant concentration. This paper proposes a vertically het...

The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats. Both dimensionally split and two-dimensional schemes are represented, as are central and upwind-biased methods, and all are at least second-order accurate.

A finite difference method is developed for solving symmetric positive differential equations in the sense of Friedrichs. The method is applicable to partial differential equations of mixed type with more general boundary conditions. The method is shown to have a convergence rate of 0(hxl2), h being the size of mesh grid. Some numerical results are presented for a model problem of forward-backw...

Direct sinrelations of smalland finite-amplitude disturbances in spatially periodic plane Poiseuille flow were performed. The ability of three high-order finite difference methods to predict the proper behavior of the disturbances was under investigation. The proposed procedure allowed to conclude about the spatial resolution and time-step required bv those schemes to produce numerically accura...

In this paper, a finite difference method for initial-boundary value problem of nonlinear Regularized-Long-Wave equation was considered. A energy conservative finite difference scheme of three levels was proposed, convergence and stability of difference solution was proved, if picking suitably,the accuracy of the new scheme is higher than others, so the method is efficient and reliable.