Exp-function method using modified Riemann-Liouville derivative for Burger's equations of fractional-order

This paper shows the combination of an efficient transformation and Exp-function method, to construct generalized solitary wave solutions of the nonlinear Burger's equations of fractional-order. Computational work and subsequent numerical results re-confirm the efficiency of the proposed algorithm. It is observed that the suggested scheme is highly reliable and may be extended to other nonlinear differential equations of fractional order

Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme

Solutions of Tenth and Ninth-order Boundary Value Problems by Modified Variational Iteration Method

In this paper, we apply the modified variational iteration method (MVIM) for solving the ninth and tenth-order boundary value problems. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method

On Inhomogeneous Fractional Partial Differential Equations

In this paper, a coupling method of Laplace transform and Homotopy analysis method is applied for solving various inhomogeneous fractional partial differential equations.The proposed algorithm presents a procedure of construct the base function and gives a high order deformation equation in simple form. The purpose of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in the other analytical techniques. The scheme is tested for some examples to demonstrate the capability of LHAM for fractional partial differential equations. Keywords: Laplace homotopy analysis method; homotopy analysis method; fractional differential equations; modified Riemann-Liouville derivative; Wave equation; Burger’s equation; Klein-Gorden equation

A Meshless Numerical Solution of the Family of Generalized Fifth-order Korteweg-de Vries Equations

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions

Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

We apply the variational iteration method using He's polynomials (VIMHP) for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007). The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method

Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM). We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique

Modified variational iteration method for a boundary layer problem in unbounded domain

Abstract: In this paper, we apply the modified variational iteration method for solving the boundary layer problem in unbounded domain. The suggested modification is made by introducing He's polynomials in the correction functional. The fact that the proposed modified variational iteration method solves nonlinear problems without using Adomian's polynomials is a clear advantage of this technique over the decomposition method

Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method

An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions