Foaming occurs in many distillation and absorption processes. The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. In this paper, we use a semi analytic method, the Adomian decomposition method, and an analytic method, the tanh method to handle the foam drainage equation. The powerful tanh method gives the solution in a closed form. However, Adomi...

where f(t),g(t), and h(t) are known continuous functions of t in the interval (0,1). Here N(u) is a nonlinear function of u. Let the above equation be singular at these two boundary value points t= 0,1. Scientists and engineers are interested in singular BVPs because they arise in a wide range of applications, such as in chemical engineering, mechanical engineering, nuclear industry, and nonlin...

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.

This paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian convex normalised fuzzy set. Using the single parametric form of fuzzy number, the original fuzz...

In the present work we consider the mathematical model that describes brain tumour growth (glioblastomas) under medical treatment. Based on the medical study presented by R. Stupp et al. (New Engl Journal of Med 352: 987996, 2005) which evidence that, combined therapies such as, radiotherapy and chemotherapy, produces negative tumour-growth, and using the mathematical model of P. K. Burgess et ...

The resolution of the reduced fractional nonlinear Schrödinger equation obtained from model describing wave propagation in left-handed transmission line presented by Djidere et al recently, allowed us this work through Adomian decomposition method (ADM) to highlight behavior and study process dark bright soliton solutions with effect derivative order as well Modulation Instability gain spectrum...

in this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. the convergence of the proposed method is given. to illustrate the proposed method, it is applied to a model for hiv infection of cd4+ t cells and the numerical results are compared with those of a recently proposed method.

Numerous applied mathematics and physical applications, such as the simulation of financial mathematics, gas dynamics, nonlinear phenomena in plasma physics, fluid mechanics, ocean engineering, utilize time-fractional generalized Burgers–Fisher equation (TF-GBFE). This describes concept dissipation illustrates how reaction systems can be coordinated with advection. To examine analyze present ev...

In this research, three numerical methods, namely the variational iteration method, Adomian decomposition and homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from classical (FW) by replacing integer-order time derivative with Caputo fractional of order η=(0,1] variable co...