Approximation Method for the Heat Equation with Derivative Boundary Conditions

In this paper, modification of Adomian decomposition method is introduced for solving heat equation with derivative boundary conditions. Some examples and the obtained results demonstrate efficiency of the proposed method. Keywords: Modified decomposition method, Heat equation, Derivative boundary conditions

A Semi-Analytic Method for Solving Two-Dimensional Fractional Dispersion Equation

In this paper, we use the analytical solution the fractional dispersion equation in two   dimensions by using modified decomposition method. The fractional derivative is described in Caputo's sense. Comparing the numerical results of method with result of the exact   solution   we   observed   that   the results correlate well. Keywords: Modified decomposition method, Fractional derivative, Fractional dispersion equation

Solutions of complex equations with adomian decomposition method

In this study, first order linear complex differential equations have been solved with adomian decomposition method.Publisher's Versio

An Efficient Sumudu Decomposition Method to Solve System of Pantograph Equations

This paper is the witness of the coupling of decomposition method with the efficient Sumudu transform known as Sumudu decomposition method to build up the exact solutions of the linear and nonlinear system of Pantograph model equations. Three mathematical models are tested to elucidate effectiveness of the method. The obtained numerical results re-confirm the potential of the proposed method. In nonlinear cases this method uses He’s Polynomials for solving the non-linear terms. It is observed that suggested scheme is highly reliable and may be extended to other highly nonlinear delay differential models. Keywords: Decomposition method, Sumudu transform, System of multi-Pantograph delay differential equations, He’s polynomial

The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method

In this paper, by introducing the fractional derivative in the sense of Caputo, we apply the Adomian decomposition method for the foam drainage equation with time- and space-fractional derivative. As a result, numerical solutions are obtained in a form of rapidly convergent series with easily computable components

Solutions of Chi-square Quantile Differential Equation

The quantile function of probability distributions is often sought after because of their usefulness. The quantile function of some distributions cannot be easily obtained by inversion method and approximation is the only alternative way. Several ways of quantile approximation are available, of which quantile mechanics is one of such approach. This paper is focused on the use of quantile mechanics approach to obtain the quantile ordinary differential equation of the Chi-square distribution since the quantile function of the distribution does not have close form representations except at degrees of freedom equals to two. Power series, Adomian decomposition method (ADM) and differential transform method (DTM) was used to find the solution of the nonlinear Chi-square quantile differential equation at degrees of freedom equals to two. The approximate solutions converge to the closed (exact) solution. Furthermore, power series method was used to obtain the solutions for other degrees of freedom and series expansion was obtained for large degrees of freedom

Approximating Solutions for Ginzburg – Landau Equation by HPM and ADM

In this paper, an analytical approximation to the solution of Ginzburg-Landauis discussed. A Homotopy perturbation method introduced by He is employed to derive the analytic approximation solution and results compared with those of the Adomian decomposition method. Two examples are presented to show the capability of the methods. The results reveal that the methods are almost equally effective and promising

Thermodynamic analysis of a variable viscosity reactive hydromagnetic couette flow within parallel plates

This investigation is to consider the impact of a temperature-dependent variable viscosity of a reactive hydromagnetic Couette fluid flowing within parallel plates. The variable property of the fluid viscosity is thought to be an exponential relation of temperature under the impact of magnetic strength. The differential equations controlling the smooth movement of fluid and energy transfer are modeled and solved by using the series solution of modified Adomian decomposition technique (mADM). The outcomes are shown in tables and graphs for different estimations of thermophysical properties present in the flow regime together with the rate of entropy generation and irreversibility distribution outcome. Keywords: Reactive fluids, Couette Flow, variable viscosity, hydromagnetic and modified Adomian decomposition method (mADM)