Natural Decomposition Method Research Articles

Numerical solution for (2 + 1)‐dimensional time‐fractional coupled Burger equations using fractional natural decomposition method

The aim of the present work is to find the numerical solutions for time‐fractional coupled Burgers equations using a new novel technique, called fractional natural decomposition method (FNDM). Two examples are considered in order to illustrate and validate the efficiency of the proposed algorithm. The numerical simulation has been conducted to ensure the exactness of the present method, and the obtained solutions are offered graphically to reveal the applicability and reliability of the FNDM. The outcomes of the study reveal that the FNDM is computationally very effective and accurate to study the (2 + 1)‐dimensional coupled Burger equations of arbitrary order.

Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method

In this work, the natural transform decomposition method (NTDM) is applied to solve the linear and nonlinear fractional telegraph equations. This method is a combined form of the natural transform and the Adomian decomposition methods. In addition, we prove the convergence of our method. Finally, three examples have been employed to illustrate the preciseness and effectiveness of the proposed method.

Natural Decomposition Approximation Solution for First Order Nonlinear Differential Equations

In this research paper, we propose the Natural decomposition method (NDM) to solve nonlinear first order differential equations. We compare the results obtained by NDM with the exact solutions. This method is a combination of the natural transform method and adomian decomposition method. By showing the less error one can be concluded that the NDM is easy to use and efficient.

Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

In this work, a combined form of the double Natural transform method with the Adomian decomposition method is developed for analytic treatment of the linear and nonlinear singular one dimensional Boussinesq equations. Two examples are provided to illustrate the simplicity and reliability of this method. Moreover, the results show that the proposed method is effective and is easy to implement for certain problems in science and engineering.

The approximate solutions of fractional gas dynamics equations by means of fractional natural decomposition method

In this work, a new practical method, which is named by the Fractional Natural Decomposition Method (FNDM), is proposed to obtain the approximate analytical solutions of fractional gas dynamics equations. The FNDM is a mixture of the Natural Transform Method and the Adomian Decomposition Method. In this method, the fractional derivatives are considered as Caputo sense and the nonlinear terms are determined by virtue of Adomian polynomials. Some test examples are given to demonstrate the efficiency and accuracy of the FNDM.

New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM

In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed.

Ramification of variable thickness on MHD TiO2 and Ag nanofluid flow over a slendering stretching sheet using NDM

The present investigation reveals the effect of variable thickness on the steady two-dimensional boundary layer flows of a TiO2-water and Ag-water nanofluid through a slendering stretching sheet. The whole analysis has been performed in the presence of variable magnetic field and variable surface temperature. Similarity transformation has been introduced to renovate the non-linear partial differential equations into ordinary ones and then they were solved using the innovative technique of Natural decomposition method (NDM). The influence of pertinent parameters on velocity and temperature distribution has been illustrated by means of graphs and tables approach. Our analysis conveys that the temperature of the nanofluid reduces due to enhancing of the variable thickness parameter. The rate of heat transfer is significantly reduced for the Ag-water nanofluid with the positive impact of nanoparticle volume fraction.

The fractional natural decomposition method: theories and applications

In this paper, we propose a new method called the fractional natural decomposition method (FNDM). We give the proof of new theorems of the FNDM, and we extend the natural transform method to fractional derivatives. We apply the FNDM to construct analytical and approximate solutions of the nonlinear time‐fractional Harry Dym equation and the nonlinear time‐fractional Fisher's equation. The fractional derivatives are described in the Caputo sense. The effectiveness of the FNDM is numerically confirmed. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical Solutions for Systems of Nonlinear Fractional Ordinary Differential Equations Using the FNDM

A new technique has been developed for analytical solutions of fractional order nonlinear ODE system. We propose a reliable method called the fractional natural decomposition method (FNDM). The FNDM is based on the natural transform method (NTM) and the Adomian decomposition method. We use the FNDM to construct new analytical approximate and exact solutions to systems of nonlinear fractional ordinary differential equation (NLFODEs). The fractional derivatives are described in the Caputo sense.

Finding exact solutions of nonlinear PDEs using the natural decomposition method

In this work, we implement the natural decomposition method (NDM) to solve nonlinear partial differential equations. We apply the NDM to obtain exact solutions for three applications of nonlinear partial differential equations. The new method is a combination of the natural transform method and the Adomian decomposition method. We prove some of the properties that are related to the natural transform method. The results are compared with existing solutions obtained by other methods, and one can conclude that the NDM is easy to use and efficient. Copyright © 2016 John Wiley & Sons, Ltd.

SOLVING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS USING THE NDM

In this research paper, we examine a novel method called the Natural Decomposition Method (NDM). We use the NDM to obtain exact solutions for three different types of nonlinear ordinary differential equations (NLODEs). The NDM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). By using the new method, we successfully handle some class of nonlinear ordinary differential equations in a simple and elegant way. The proposed method gives exact solutions in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlinear differential equation. One can conclude that the NDM is efficient and easy to use.

SOLVING COUPLED SYSTEM OF NONLINEAR PDE'S USING THE NATURAL DECOMPOSITION METHOD

In this research paper, we develop a new method called the Natural Decomposition Method (NDM) for solving coupled system of nonlinear partial differential equations (CSNLPDEs). The new method is a combination of the Natural Transform Method (NTM) and the Adomian Decomposition Method (ADM). By using the new method, we successfully handle some class of cou- pled system of nonlinear partial differential equations (CSNLPDEs) in a simple and elegant way. The proposed method gives an exact or approximate solution in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlin- ear differential equation. Thus, NDM can easily be used to solve a wide class of nonlinear partial differential equations (NLPDEs) and obtain an exact or analytical solution.

A new approach to linear and nonlinear Schrodinger equations using the natural decomposition method

A new approach to linear and nonlinear Schrodinger equations using the natural decomposition method

An efficient technique for solving gas dynamics equation using the natural decomposition method

In this paper, we introduce a new technique called the Natural Decomposition Method (NDM) for solving homogeneous and inhomogeneous gas dynamic equations. The new method is an elegant combination of the Natural transform Method (NTM) and Adomian Decomposition Method (ADM). The proposed method is applied directly without using linearization, transformation, discretization or taking some restrictive assumptions. Using the new method, we successfully obtain exact solution of two illustrative examples, and the results are compared with the results of the existing methods. This shows the reliability, accuracy, and efficiency of the new method.

Exact solution of equation governing the unsteady flow of a polytropic gas using the natural decomposition method

In this article, we introduced a new technique called the Natural Decomposition Method (NDM) for solving the equation governing the unsteady flow of a polytropic gas. The new technique is a combination of the Natural transform Method (NTM) and Adomian Decomposition Method (ADM). The proposed technique is applied directly without using any linearization, discretization, transformation, or taking some restrictive assumptions and it drastically reduce the computational size. Using the new technique, we successfully obtained exact solution of the nonlinear equations governing the unsteady flow of a polytropic gas, and the results are compared with the results of the existing methods. This shows the simplicity, efficiency, reliability and accuracy of the new technique.

Identifying the Potential Influences on Income Inequality Changes in Korea - Income Factor Source Analysis

This study attempts to measure what effects the direction and size of contributions of a number of different income sources at the household level has on the changes in inequality indexes in Korea between 1988 and 2002. Based on the Urban Household Income and Expenditure Survey (UHIES) from the National Statistics Office (NSO), it is found that the household head wage income has a decreasing effect on inequality, whereas the wage income from spouses and other members of households seem to increase the level of inequality at the household level, where the magnitude of such an effect on market income inequality is far smaller than that of the household head wage income. However, due to the inherent limitations of UHIES, generalizing the empirical findings to all types of households becomes questionable. The analytical tool used in this study is based on Shorrocks' natural decomposition method (1982, 1983) and Lerman and Yitzhaki's (1985) Gini decomposition method.

A natural domain decomposition method with non-matching grids

In this paper a natural domain decomposition method based on local Dirichlet–Neumann maps is considered. The global variational problem is defined on the skeleton of the domain decomposition only. For the approximation of the Dirichlet–Neumann maps Dirichlet boundary value problems need to be solved locally. The local finite element spaces within the subdomains can be chosen independently of the global trial space on the skeleton. In particular, this approach can be used to couple non-matching triangulations across the interfaces without an additional framework such as introducing Lagrange multipliers. Numerical results for two model problems confirm the stability and error estimates given here.

Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods

In this paper we consider domain decomposition methods for solving the radial basis function interpolation equations. There are three interwoven threads to the paper. The first thread provides good ways of setting up and solving small- to medium-sized radial basis function interpolation problems. These may occur as subproblems in a domain decomposition solution of a larger interpolation problem. The usual formulation of such a problem can suffer from an unfortunate scale dependence not intrinsic in the problem itself. This scale dependence occurs, for instance, when fitting polyharmonic splines in even dimensions. We present and analyze an alternative formulation, available for all strictly conditionally positive definite basic functions, which does not suffer from this drawback, at least for the very important example previously mentioned. This formulation changes the problem into one involving a strictly positive definite symmetric system, which can be easily and efficiently solved by Cholesky factorization. The second section considers a natural domain decomposition method for the interpolation equations and views it as an instance of von Neumann's alternating projection algorithm. Here the underlying Hilbert space is the reproducing kernel Hilbert space induced by the strictly conditionally positive definite basic function. We show that the domain decomposition method presented converges linearly under very weak nondegeneracy conditions on the possibly overlapping subdomains. The last section presents some algorithmic details and numerical results of a domain decomposition interpolatory code for polyharmonic splines in 2 and 3 dimensions. This code has solved problems with 5 million centers and can fit splines with 10,000 centers in approximately 7 seconds on very modest hardware.

Concurrent regular expressions and their relationship to Petri nets

We define algebraic systems called concurrent regular expressions which provide a modular description of languages of Petri nets. Concurrent regular expressions are extension of regular expressions with four operators - interleaving, interleaving closure, synchronous composition and renaming. This alternative characterization of Petri net languages gives us a flexible way of specifying concurrent systems. Concurrent regular expressions are modular and, hence, easier to use for specification. The proof of equivalence also provides a natural decomposition method for Petri nets.