Volume 5, Issue 4

The major cause of the Hawaiian Islands coastal erosion is shown to be not global warming, but the sinking of the volcanic islands. The geologic “circle-of-life” beyond the Hawaiian hot spot is the true explanation of the beach erosion. The sea levels are slow rising and not accelerating worldwide as well as in the United States. In the specific of the Hawaii Islands, they have been decelerating over the last 3 decades because of the phasing of the multi-decadal oscillations for this area of the Pacific. There is therefore no evidence coastal erosion will double in the Hawaii by 2050 because of global warming.

We present an analytic algorithm to solve the generalized Berger-Fisher (B-F) equation, B-F equation, generalized Fisher equation and Fisher equation by using residual power series method (RPSM), which is based on the generalized Taylor’s series formula together with the residual error function. In all the cases obtained results are verified through the different graphical representation. Comparison of the results obtained by the present method with exact solution reveals that the accuracy and fast convergence of the proposed method.

In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers’ equation. The Burgers’ equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.

The chemical reaction, Soret and Dufour effects on steady flow of a couple stress fluid between two rotating disks are studied. The lower disc is rotating with angular velocity Ω 1 where as the upper disc is rotating with Ω 2 . The density variation in centrifugal and Coriolis force terms are taken into consideration by invoking a linear density-temperature relation and Boussinesq approximation to account the buoyancy effects. The non-linear governing partial differential equations are transformed into system of ordinary differential equations by using the similarity transformations. Homotopy Analysis Method (HAM) has been used to solve the resulting equations. Graphical illustrations of the dimensionless velocity, concentration and temperature profiles are presented at different values of the emerging parameter of the present study. It has been found that as an increase in couple stresses leads to the decrease in velocity, temperature and increase in concentration of the fluid. Flow velocities, temperature and concentration profiles are decreases with an increase in reaction parameter.

In this paper we investigate the control of three-dimensional non-autonomous fractional-order model of a permanent magnet synchronous motor (PMSM) and PI controlled fractional order Induction motor via recursive extended back stepping control technique. A robust generalized weighted controllers are derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results.

In this paper, we study a dynamical Brusselator reaction-diffusion system arising in triple collision and enzymatic reactions with time fractional Caputo derivative. The present article involves a more generalized effective approach, proposed for the Brusselator system say q -homotopy analysis transform method ( q -HATM), providing the family of series solutions with nonlocal generalized effects. The convergence of the q -HATM series solution is adjusted and controlled by auxiliary parameter ℏ and asymptotic parameter n . The numerical results are demonstrated graphically. The outcomes of the study show that the q -HATM is computationally very effective and accurate to analyze nonlinear fractional differential equations.

In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.