Reconstruction Of Variational Iteration Method Research Articles

Solving the general form of the fractional Black–Scholes with two assets through Reconstruction Variational Iteration Method

Solving the general form of the fractional Black–Scholes with two assets through Reconstruction Variational Iteration Method

Analytical Solution of Biological Population of Fractional Differential Equations by Reconstruction of Variational Iteration Method

This article presents a brand-new approximation analytical technique we refer to as the reconstruction of variational iteration method. For the goal of solving fractional biological population option pricing equations, this methodology was created. In certain circumstances, you may actually use the well-known Mittag-Leffer function to get an explicit response. The usage of the three examples below demonstrates the precision and effectiveness of the suggested method. The results show that the RVIM is not only quite straightforward but also very successful at resolving non-linear problems.

ANALYSIS OF DYNAMIC BEHAVIOUR OF FRACTIONAL ORDER SIR EPIDEMIC MODEL OF CHILDHOOD DISEASES USING RVIM

In the given article, the solution of a Mathematical Model of epidemic in childhood diseases is presented. Reconstruction of Variational Iteration Method (RVIM) is used to analyze the model which inculcates the Laplace Transform to reconstruct VIM. This technique is generally used to get solutions of fractional differential equations of linear and non linear form. The result obtained has been simulated and discussed through graphs.

The effect of local thermal nonequilibrium on conduction in metal foam tube heat exchanger with a uniform heat source

The effect of local thermal nonequilibrium on the steady state heat conduction in metal foam tube heat exchanger as a porous layer in the presence of internal heat generated by considering the thermal conductivity coefficient as a function of temperature was investigated. A two temperature model is investigated by using reconstruction of variational iteration method (RVIM). The obtained results from RVIM are compared with the numerical results of Maple. These comparisons reveal that RVIM is a very powerful and precise approach to solve nonlinear ordinary differential equations and there is a good agreement between them. In this study, the effects of porosity and internal heat generation on the temperature distribution in the solid and liquid phases are presented.

MHD copper-water nanofluid flow and heat transfer through convergent-divergent channel

This work is focused on the analytical solution of a nanofluid consisting of pure water with copper nanoparticle steady flow through convergent-divergent channel. The velocity and temperature distributions are determined by a novel method called Reconstruction of variational iteration method (RVIM). The effects of angle of the channel, Reynolds and Hartmann numbers on the nanofluid flow are then investigated. The influences of solid volume fraction and Eckert number upon the temperature distribution are discussed. Based on the achieved results, Nusselt number enhances with increment of solid volume fraction of nanoparticles, Reynolds and Eckert numbers. Also the fourth order Runge-Kutta method, which is one of the most relevant numerical techniques, is used to investigate the validity and accuracy of RVIM and good agreement is observed between the solutions obtained from RVIM and some known numerical results.

On the convergence of a new reliable algorithm for solving multi-order fractional differential equations

In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods.

Solving Fractional Partial Differential Equations with Variable Coefficients by the Reconstruction of Variational Iteration Method

Abstract In this article, we propose a new approach for solving fractional partial differential equations with variable coefficients, which is very effective and can also be applied to other types of differential equations. The main advantage of the method lies in its flexibility for obtaining the approximate solutions of time fractional and space fractional equations. The fractional derivatives are described based on the Caputo sense. Our method contains an iterative formula that can provide rapidly convergent successive approximations of the exact solution if such a closed form solution exists. Several examples are given, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

Go-water nanofluid inside semi porous channel: analytical investigation

This paper concerns the analytical investigation of the GO-water nanofluid flow in a semi-porous channel. The Similarity Berman’s transformation is employed to convert the governing partial differential equations of a steady laminar flow of an electrically conducting fluid in a two dimensional channel. Reconstruction of Variational Iteration Method (RVIM) has been used to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity fields. The results indicated that the Reynolds number, Hartmann number and solid volume fraction have strong effect on velocity boundary layer thickness.

Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation

Abstract In this article, we have implemented reconstruction of variational iteration method as a new approximate analytical technique for solving fractional Black-Scholes option pricing equations. Indeed, we essentially use the well-known Mittag-Leffler function to obtain explicit solutions for some examples of financial mathematics equations.

A New Reconstruction of Variational Iteration Method and Its Application to Nonlinear Volterra Integrodifferential Equations

We reconstruct the variational iteration method that we call, parametric iteration method (PIM). The purposed method was applied for solving nonlinear Volterra integrodifferential equations (NVIDEs). The solution process is illustrated by some examples. Comparisons are made between PIM and Adomian decomposition method (ADM). Also exact solution of the 3rd example is obtained. The results show the simplicity and efficiency of PIM. Also, the convergence of this method is studied in this work.

Dynamic Analysis of a Micro-Cantilever Subjected to Harmonic Base Excitation via RVIM

In this paper, dynamic analysis of a cantilever beam with micro-scale dimensions is presented. The micro-cantilever is subjected to harmonic base excitation and constant force at micro-cantilever tip. By Euler-Bernoulli beam theory assumptions, the mathematical formulation of vibrating micro-cantilever beam is derived using extended Hamilton principle. The governing partial-diffrential equation is solved by reconstruction of variational iteration method (RVIM), with possession of its boundary conditions. The RVIM is an approximate method of solving that answers easy and quick and has high accuracy.

A New Modified Approach For Solving Seven-order Sawada-kotara Equations

Herein, Reconstruction of Variational Iteration Method (RVIM) is used for computing solutions of the seventh-order Sawada-Kotera equation (sSK) and a Lax’s seventh order KdV equations (LsKdV). The results are compared with the Adomian decomposition method (ADM) and the known analytical solutions. Results obtained expose effectiveness and capability of this method to solve the seven-order Sawada-Kotera (sSK) and a Lax's seven-order KdV (LsKdV) equations.

A Novel Iterative Method for Solving Systems of Fractional Differential Equations

The Reconstruction of Variational Iteration Method (RVIM) technique has been successfully applied to obtain solutions for systems of nonlinear fractional differential equations: , ,  , , where denote Caputo fractional derivative. The RVIM, for differential equations of integer order is extended to derive approximate analytical solutions for systems of fractional differential equations. Advantage of the RVIM, is simplicity of the computations and convergent successive approximations without any restrictive assumptions or transform functions. Some illustrative examples are given to show the validity of this method for solving linear and nonlinear systems of fractional differential equations.

Analytical Investigation of Jeffery-Hamel Flow with High Magnetic Field and Nano Particle by RVIM

Many researchers have been interested in application of mathematical methods to find analytical solutions of nonlinear equations and for this purpose, new methods have been developed. One of the newest analytical methods to solve nonlinear equations is Reconstructio n of variational Iteration Method (RVIM) which is an accurate and a rapid convergence method in finding the approximate solution for nonlinear equations. By applying Laplace Transform, RVIM overcomes the difficulty of the perturbation techniques and other variational methods in case of using small parameters and Lagrange multipliers, respectively. In this study RVIM is applied for the effects of magnetic field and nano particle on the Jeffery-hamel flow. The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. Finally the effect of nano particle volume fraction in the absence of magnetic field is investigated, too. The validity of RVIM method is ascertained by comparing our results with numerical (Runge Kutta method) results.

Approximate traveling wave solution for shallow water wave equation

Reconstruction of Variational Iteration Method (RVIM) is used for computing the coupled Whitham–Broer–Kaup shallow water. Then RVIM solution is verified against exact one and is compared with powerful approximate solutions, the Homotopy Perturbation Method (HPM) and Homotopy Analysis Method (HAM). The existent error of the methods is computed and convergence of the RVIM solution has been presented. Results obtained expose effectiveness and capability of this method to solve the nonlinear systems in mechanics, analytically.