Volume 5, Issue 2

The present study investigates the heat transfer in an electrically conducting Oldroyd-B fluid through a channel with stretchingwalls in the presence of an applied magnetic field. The governing partial differential equations are reduced in a set of nonlinear ordinary differential equations using dimensionless variables. An implicit finite difference method is employed to develop a numerical solution at each spatial node for the governing nonlinear differential equations. The obtained results are analyzed and discussed graphically under the influence of controlling pertinent parameters.

The aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order.

The capacity and effectiveness of a modified variational approach, namely global error minimization (GEM) is illustrated in this study. For this purpose, the free oscillations of a rod rocking on a cylindrical surface and the Duffing-harmonic oscillator are treated. In order to validate and exhibit the merit of the method, the obtained result is compared with both of the exact frequency and the outcome of other well-known analytical methods. The corollary reveals that the first order approximation leads to an acceptable relative error, specially for large initial conditions. The procedure can be promisingly exerted to the conservative nonlinear problems.

In this paper, some sufficient conditions for uniform practical stability of impulsive functional differential equations in terms of two measures with effect of delay at the time of impulses are obtained by using piecewise continuous Lyapunov functions and Razumikhin techniques. The application of obtained result is illustrated with an example.

The characteristics of the unsteady boundary layer flow with melting heat transfer near a stagnation-point towards a flat plate embedded in a DarcyBrinkman porous medium with thermal radiation are investigated. The governing partial differential equations are transformed into self-similar ordinary differential equations by similarity transformations. The transformed self-similar equations are solved numerically using bvp4c from Matlab for several values of the flow parameters. The study reveals that the multiple solutions exist for the decelerating ( A < 0) flow, whereas for the accelerating ( A ≥ 0) flow, the solution is unique. The results also indicate that the melting phenomenon increases the rate of heat transfer and delays the boundary layer separation. To validate the current numerical results, comparison with available results is made and found to be in a good agreement.

This paper applied the idea of block pulse (BP) transform in the equivalent linearization of a nonlinear system. The BP transform gives effective tools to approximate complex problems. The main goal of this work is on using BP transform properties in process of linearization. The accuracy of the proposed method compared with the other equivalent linearization including the stochastic equivalent linearization and the regulation linearization methods. Numerical simulations are applied to the nonlinear Van der Pol oscillator system under Gaussian white noise excitation to demonstrate the feasibility of the present method. Different values of nonlinearity are considered to show the effectiveness of the present method. Besides, by comparing the mean-square responses for divers values of nonlinearity and excitation intensity depicted the present method is able to approximate the behavior of nonlinear system and is in agreement with other methods.

The tide gauges measure the local oscillations of the sea level vs. the tide gauge instrument. The tide gauge instrument is generally subjected to the general subsidence or uplift of the nearby inland, plus some additional subsidence for land compaction and other localised phenomena. The paper proposes a non-linear model of the relative sea level oscillations including a long term trend for the absolute sea level rise, another term for the subsidence of the instrument, and finally a sinusoidal approximation for the cyclic oscillations of periodicities up to decades. This non-linear model is applied to the tide gauges of China. The paper shows that the limited information available for China does not permit to infer any proper trend for the relative rates of rise, as the tide gauge records are all short or incomplete and the vertical movement of the tide gauge instruments is unassessed. The only tide gauge record of sufficient length that may be assembled for China is obtained by combining the North Point and Quarry Bay tide gauges in Hong Kong (NPQB). This NQPB composite tide gauge record is shown to have similarities with the tide gauge records of Sydney, equally in the West pacific, and San Diego, in the east Pacific, oscillating about the longer term trend mostly determined by the local subsidence. As it is very well known that China generally suffers of land subsidence, and the tide gauge installations may suffer of additional subsidence vs. the inland, it may be concluded from the analysis of the other worldwide tide gauges that the sea levels of China are very likely rising about the same amount of the subsidence of the tide gauges, with the sea level acceleration component still negligible.

The object of the present article is to study spacefractional telegraph equation by fractional Homotopy perturbation transform method (FHPTM). The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm. Three test examples are presented to show the efficiency of the proposed technique.