Decomposition method for solving parabolic equations in finite domains

This paper presents a comparison among Adomian decomposition method (ADM), Wavelet-Galerkin method (WGM), the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method (BTCS), (7,7) Crank-Nicholson type finite difference formula (C-N), the fully explicit method (1,13) and 9-point finite difference method, for solving parabolic differential equations with arbitrary boundary conditions and based on weak form functionals in finite domains. The problem is solved rapidly, easily and elegantly by ADM. The numerical results on a 2D transient heat conducting problem and 3D diffusion problem are used to validate the proposed ADM as an effective numerical method for solving finite domain parabolic equations. The numerical results showed that our present method is less time consuming and is easier to use than other methods. In addition, we prove the convergence of this method when it is applied to the nonlinear parabolic equation.

Adomian decomposition method simulation of von Kármán swrling bioconvection nanofluid flow

The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.

Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem

In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.

On study of horizontal thin film flow of Sisko fluid due to surface tension gradient

The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.

Adomian decomposition method for Hall and ion-slip effects on mixed convection flow of a chemically reacting Newtonian fluid between parallel plates with heat generation/absorption

This paper analyzes the heat and mass transfer characteristics on mixed convective fully developed flow in an electrically conducting Newtonian fluid between vertical parallel plates.The chemical reaction,heat generation,Hall and ion-slip effects are taken into consideration.By using similarity transformations the nonlinear governing equations are reduced into dimensionless form and hence solved using Adomian decomposition method(ADM).The influence of magnetic parameter,Hall parameter,ion-slip parameter,chemical reaction parameter,and heat generation/absorption parameter on non-dimensional velocities,temperature and concentration profiles are exhibited graphically.In addition,the numerical data for skin friction,heat and mass transfer rates are shown in tabular form.

Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel

In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.

Thermodynamic analysis for a third grade fluid through a vertical channel with internal heat generation

This paper makes the thermodynamic analysis in forced convective flow of a third grade fluid through a vertical channel. Due to the reactive nature of the fluid, the effect of internal heat generation is considered and assumed to be a linear function of temperature. The coupled nonlinear dimensionless ordinary differential equations governing the fluid flow are solved by using the Adomian decomposition method（ADM）. The effects of various physical parameters such as third grade material parameter, buoyancy parameter and heat generation parameter on the thermal structure of flow are presented and discussed.

Numerical analysis approach for models of COVID-19 and other epidemics

The world wide spread of COVID-19 epidemic has instigated an unprecedented demand and supply of research related to this epidemic.Together with medical research for treatment and cure of the pandemic,efficient mathematical modeling of epidemics is the need of hour.First,this paper depicts a detailed and comprehensive compendium of various numerical methods used for infectious diseases modeling during last 14 years including the very recent work done for COVID-19 models.This gives researchers a good insight about past work done,present efforts and future scope of numerical analysis methods for epidemic modeling.Second,this paper also proposes its numerical analysis approach based on Adomian decomposition method(ADM)for generalized SEIR model of COVID-19.The proposed method is shown to give very accurate numerical results.

Unsteady thin film flow of a fourth grade fluid over a vertical moving and oscillating belt

This article studies the unsteady thin film flow of a fourth grade fluid over a moving and oscillating vertical belt.The problem is modeled in terms of non-nonlinear partial differential equations with some physical conditions.Both problems of lift and drainage are studied.Two different techniques namely the adomian decomposition method(ADM)and the optimal homotopy asymptotic method(OHAM)are used for finding the analytical solutions.These solutions are compared and found in excellent agreement.For the physical analysis of the problem,graphical results are provided and discussed for various embedded flow parameters.