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

Latest Developments in Nonlinear Sciences

This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim

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

Variational Iteration Method for Solving Initial and Boundary Value Problems of Bratu-type

In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm

On the Solution of the Vibration Equation by Means of the Homotopy Perturbation Method

In this paper, we present a reliable algorithm, the homotopy perturbation method, to solve the well-known vibration equation for very large membrane which is given initial conditions. By using initial value, the explicit solutions of the equation for different cases have been derived, which accelerate the rapid convergence of the series solution. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to differential equations. Numerical results for different particular cases of the problem are presented graphically

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

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

On Numerical Solutions of Two-Dimensional Boussinesq Equations by Using Adomian Decomposition and He\u27s Homotopy Perturbation Method

In this paper, we obtain the approximate solution for 2-dimensional Boussinesq equation with initial condition by Adomian\u27s decomposition and homotopy perturbation methods and numerical results are compared with exact solutions