In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using Caputo fractional derivative. We solve non-linear fractional-order system containing six differential equations understand ASR. For proving existence unique solution, use some recent novel properties Mittag–Leffler function along with fixed point theory. The stability proposed is als...

We consider the weak analogues of certain strong stochastic numerical schemes considered in [10], namely a Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computation...

The bidomain model is a system of partial differential equations used to model the propagation of electrical potential waves in the myocardium. It is composed of coupled parabolic and elliptic partial differential equations, as well as at least one ordinary differential equation to model the ion activity through the cardiac cell membranes. The purpose of this paper is to propose and analyze sev...

in previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. then we extendedthis research to the simulation of continuous fuzzy systems models. in this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. consider a crisp continuous system whose evolution depends ondifferential equations. such a ...

We introduce different high order time discretization schemes for backward semi-Lagrangian methods. These schemes are based on multi-step schemes like AdamsMoulton and Adams-Bashforth schemes combined with backward finite difference schemes. We apply these methods to transport equations for plasma physics applications and for the numerical simulation of instabilities in fluid mechanics. In the ...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...

We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have been used as higher-order initial value problem solvers for over a century. Fur...

In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...

A numerical model used to simulate global convection and magnetic field generation in stars is described. Nonlmear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical, fluid shell heated from below. The velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resol...

Regenerative chatter is the most important factor affecting stability of milling process. It core for suppressing and improving production efficiency to accurately efficiently identify stable region chatter. Therefore, according theory predictor-corrector, three predictor–corrector methods (PCM) are, respectively, proposed by applying fourth-order Adams-Bashforth-Moulton formula, Simpson Hammin...