The paper must have abstract. In this paper, we present an approximate analytical algorithm to solve non-linear quadratic Riccati differential equations of fractional order based on the optimal homotopy asymptotic method (OHAM). OHAM has the benefit of adjusting the convergence rate and the region of the solution series via several auxiliary parameters over the homotopy analysis method (HAM) th...

In this paper, I explore the solution of the contaminant transport problem over a random conductivity field. First, I generate a random, correlated conductivity field by convolving independent, uniformly distributed random variables with the identity function. I use finite differences to discretize the diffusion equation to solve for the steady-state pressure gradient using Backward Euler. This...

In this paper, a highly accurate method is introduced to achieve the numerical solution of advection diffusion equation (ADE). This approach contains collocation technique based on nonic B-spline functions in spatial-domain discretization and Adams Moulton scheme temporal-domain discretization. Two test problems are studied validate effectiveness new presented efficiency approximate results tes...

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...

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores complexity and synchronization of a fractional-order laser dynamical model. The dynamics under variance derivative order q parameters system have examined using multiscale algorithm bifurcation diagram. Numerical simulation outcomes demonstrate that generates chaos with decreasing q. Moreover, designs coupled network syst...

The three-point fully implicit block methods are developed for solving large systems of ordinary differential equations using variable step size on a parallel shared memory computer. The methods calculate the numerical solution at three points simultaneously and are suitable for parallelization across the method. The methods are in a simple form as Adams Moulton method with the specific aim of ...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM was utilized establish approximate series solutions. technique considered be an extension original Adams–Bashforth–Moulton approach. Numerical simulations and figures are discussed, in order show efficiency of proposed method. futur...