5 research outputs found
Solutions of complex equations with adomian decomposition method
In this study, first order linear complex differential equations have been solved with adomian decomposition method.Publisher's Versio
Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method
The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. Very recently, a novel way was proposed by Duan (2010) to calculate the Adomian series which is a crucial step of the Adomian decomposition method. In this paper, it was used to solve some fractional nonlinear differential equations
The adomian decomposition method applied to blood flow through arteries in the presence of a magnetic field
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. February 16, 2015.The Adomian decomposition method is an effective procedure for the
analytical solution of a wide class of dynamical systems without linearization
or weak nonlinearity assumptions, closure approximations, perturbation
theory, or restrictive assumptions on stochasticity. Our aim here is to apply
the Adomian decomposition method to steady two-dimensional blood
flow
through a constricted artery in the presence of a uniform transverse magnetic
field. Blood
flow is the study of measuring blood pressure and determining
flow through arteries. Blood
flow is assumed to be Newtonian and is governed
by the equation of continuity and the momentum balanced equation (which
are known as the Navier-Stokes equations). This model is consistent with
the principles of ferro-hydrodynamics and magnetohydrodynamics and takes
into account both magnetization and electrical conductivity of blood. We
apply the Adomian decomposition method to the equations governing blood
flow through arteries in the presence of an external transverse magnetic field.
The results show that the e ect of a uniform external transverse magnetic
field applied to blood
flow through arteries favors the physiological condition
of blood. The motion of blood in stenosed arteries can be regulated by
applying a magnetic field externally and increasing/decreasing the intensity
of the applied field
Two Reliable Methods for Solving the (3 + 1)-Dimensional Space-Time Fractional Jimbo-Miwa Equation
We investigate methods for obtaining exact solutions of the (3 + 1)-dimensional nonlinear space-time fractional Jimbo-Miwa equation in the sense of the modified Riemann-Liouville derivative. The methods employed to analytically solve the equation are the G′/G,1/G-expansion method and the novel G′/G-expansion method. To the best of our knowledge, there are no researchers who have applied these methods to obtain exact solutions of the equation. The application of the methods is simple, elegant, efficient, and trustworthy. In particular, applying the novel G′/G-expansion method to the equation, we obtain more exact solutions than using other existing methods such as the G′/G-expansion method and the exp-Φ(ξ)-expansion method. The exact solutions of the equation, obtained using the two methods, can be categorized in terms of hyperbolic, trigonometric, and rational functions. Some of the results obtained by the two methods are new and reported here for the first time. In addition, the obtained exact explicit solutions of the equation characterize many physical meanings such as soliton solitary wave solutions, periodic wave solutions, and singular multiple-soliton solutions