Asif Waheed

VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS

In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite ecient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restric- tive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlin- ear problems without using the Adomians polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and eciency of the proposed method. Comparisons are made to reconfirm the eciency and accuracy of the suggested technique.

Exp-Function Method for Generalized Travelling Solutions of Calogero-Degasperis-Fokas Equation

Abstract In this paper, we apply a relatively new technique which is called the exp-function method to construct generalized solitary and periodic solutions of Calogero-Degasperis-Fokas (CDF) equation which plays a very important role in mathematical physics, applied and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. Numerical results clearly indicate the reliability and efficiency of the proposed method.

Exp-function method for traveling wave solutions of nonlinear evolution equations

In this paper, we apply the exp-function method to construct generalized solitary and periodic solutions of nonlinear evolution equations. The proposed technique is tested on the modified Zakharov-Kuznetsov (ZK) and Zakharov-Kuznetsov-Modified-Equal-Width (ZK-MEW) equations. These equations play a very important role in mathematical physics and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. Numerical results clearly indicate the reliability and efficiency of the proposed exp-function method.

Some new solitonary solutions of the modified Benjamin–Bona–Mahony equation

Abstract In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results.

On Combined Effects of Heat Transfer and Chemical Reaction for the Flow through an Asymmetric Channel with Orthogonally Deformable Porous Walls

The combined effects of heat transfer and chemical reaction are studied for the flow through a semi-infinite asymmetric channel with orthogonally deformable porous walls. The similarity transforms have been used to reduce the conservation laws to a corresponding system of nonlinear ordinary differential equations. The resulting equations are solved, both analytically and numerically, by using Homotopy Analysis Method (HAM) and the fourth-order Runge-Kutta (RK-4) method, respectively. The convergence of the analytical solution is assured through the so-called total squared residual error analysis. The optimal values of auxiliary parameters are obtained by minimizing the total squared residual error.

An Efficient Method for Solving System of Third-Order Nonlinear Boundary Value Problems

we use the modified variation of parameters method for finding the analytical solution of a system of third-order nonlinear boundary value problems associated with obstacle, unilateral, and contact problems. The results are calculated in terms of convergent series with easily computable components. The suggested technique is applied without any discretization, perturbation, transformation, and restrictive assumptions. Moreover, it is free from round off errors. Some examples are given to illustrate the implementation and efficiency of the modified variation of parameters method.

Numerical solution of contaminated oil along a vertical wavy frustum of a cone

The effect of wavy surface on natural convection flow of two-phase dusty fluid over a vertical frustum of a cone is presented in this paper. The boundary layer regime having the large value of Grashof number Gr is considered and the wavy surface is assume to have wavelength and amplitude of O(1). A sinusoidal surface is used as a particular example to elucidate the heat transfer mechanism near such surfaces. The transformed boundary layer equations are solved numerically and detailed results for the skin friction and rate of heat transfer coefficients are presented for a selected parameters: wavy surface amplitude, half cone angle, mass concentration parameter and dust parameter. Comprehensive flow formations of the contaminated oil having Pr equal to 500.0, are given with the aim to predict the enhancement of heat transport across the heated wavy frustum of the cone.

VARIATION OF PARAMETERS METHOD FOR SOLVING A CLASS OF EIGHTH-ORDER BOUNDARY-VALUE PROBLEMS

In this paper, we use the variation of parameters method to solve a class of eighth-order boundary-value problems. The analytical results are calculated in terms of convergent series. Error estimates are tabulated and are compared with some other well known techniques which reveal the complete reliability of the suggested scheme. Several examples are given to verify the reliability and efficiency of the proposed method.