Volume 5, Issue 1

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

The aim of the present work is to propose a simple and reliable algorithm namely homotopy perturbation transform method (HPTM) for KdV equations in warm plasma. The homotopy perturbation transform method is a combined form of the Laplace transform method with the homotopy perturbation method. In this method, the solution is calculated in the form of a convergent series with an easily computable compact. To illustrate the simplicity and reliability of the method, several examples are provided. In this paper, the homotopy perturbation transform method has been applied to obtain the solution of the KdV, mKdV, K(2, 2) and K(3,3) equations. We compared our solutions with the exact solutions. Results illustrate the applicability, efficiency and accuracy of HPTM to solve nonlinear equations despite needlessness to any linearization or perturbation. It is predicted that the proposed algorithm can be widely applied to other nonlinear problems in science and engineering.

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers’ equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He’s polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.

The flow of an incompressible fractionalized Maxwell fluid induced by an oscillating plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and the associated shear stress, written in terms of H-functions, using discrete Laplace transform, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter θ → 0. Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The solutions for fractionalized and ordinary Maxwell fluids for noslip condition also obtained as a special cases and they are similar to the solutions of classical Stokes’ first problem of fractionalized and ordinary Maxwell fluid, if oscillating parameter ω = 0. Finally, the influence of the material, slip and the fractional parameters on the fluid motion, as well as a comparison among fractionalized Maxwell, ordinary Maxwell and Newtonian fluids is also analyzed by graphical illustrations.

The sea levels of Kiribati have been stable over the last few decades, as elsewhere in the world. The Australian government funded Pacific Sea Level Monitoring (PSLM) project has adjusted sea level records to produce an unrealistic rising trend. Some information has been hidden or neglected, especially from sources of different management. The measured monthly average mean sea levels suffer from subsidence or manipulation resulting in a tilting from the about 0 (zero) mm/year of nearby tide gauges to 4 (four) mm/year over the same short time window. Real environmental problems are driven by the increasing local population leading to troubles including scarcity of water, localized sinking and localised erosion.

Contrary to what is claimed by reconstructions of the Global Mean Sea Level (GMSL) indicating accelerating sea level rates of rise over the twentieth-century, the actual measurements at the tide gauges show the sea levels have not risen nor accelerated that much. The most recent estimation by Hay et al [1] of the twentieth-century global mean sea level (GMSL) rise is the last attempt to give exact reconstructions without having enough information of the state of the world oceans over a century where unfortunately the good measurements were not that many. The information on relative rates of rise at the tide gauges and land subsidence of global positioning system (GPS) domes suggest the relative rate of rise is about 0.25mm/year, without any detectable acceleration. [The naïve average of all the world tide gauges of sufficient quality and length of the Permanent Service to Mean Sea Level (PSMSL) data base], Both the relative rates of rise at the tide gauges and the land vertical velocity of GPS domes of the Système d’Observation du Niveau des Eaux Littorales (SONEL) data base are strongly variable in space and time to make a nonsense the GMSL estimation.