1,022 research outputs found
An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method
In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition
method (ADM) is generalized to find positive solutions for boundary value problems involving nonlinear fractional
ordinary differential equations. In the proposed algorithm the boundary conditions are used to convert the nonlinear
fractional differential equations to an equivalent integral equation and then a recursion scheme is used to obtain the
analytical solution components without the use of undetermined coefficients. Hence, there is no requirement to solve
a nonlinear equation or a system of nonlinear equations of undetermined coefficients at each stage of approximation
solution as per in the standard ADM. The fractional derivative is described in the Caputo sense. Numerical examples
are provided to demonstrate the feasibility of the proposed algorithm
Laplace Adomian Decomposition Method to study Chemical ion transport through soil
The paper deals with a theoretical study of chemical ion transport in soil under a uniform external force in the transverse direction, where the soil is taken as porous medium. The problem is formulated in terms of boundary value problem that consists of a set of partial differential equations, which is subsequently converted to a system of ordinary differential equations by applying similarity transformation along with boundary layer approximation. The equations hence obtained are solved by utilizing Laplace Adomian Decomposition Method (LADM). The merit of this method lies in the fact that much of simplifying assumptions need not be made to solve the non-linear problem. The decomposition parameter is used only for grouping the terms, therefore, the nonlinearities is handled easily in the operator equation and accurate approximate solution are obtained for the said physical problem. The computational outcomes are introduced graphically. By utilizing parametric variety, it has been demonstrated that the intensity of the external pressure extensively influences the flow behavior
Series solution of the time-dependent Schr\"{o}dinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method
The Schr\"{o}dinger-Newton model is a nonlinear system obtained by coupling
the linear Schr\"{o}dinger equation of canonical quantum mechanics with the
Poisson equation of Newtonian mechanics. In this paper we investigate the
effects of dark energy on the time-dependent Schr\"{o}dinger-Newton equations
by including a new source term with energy density , where is the cosmological constant, in addition to the
particle-mass source term . The resulting
Schr\"{o}dinger-Newton- (S-N-) system cannot be solved
exactly, in closed form, and one must resort to either numerical or
semianalytical (i.e., series) solution methods. We apply the Adomian
Decomposition Method, a very powerful method for solving a large class of
nonlinear ordinary and partial differential equations, to obtain accurate
series solutions of the S-N- system, for the first time. The dark
energy dominated regime is also investigated in detail. We then compare our
results to existing numerical solutions and analytical estimates, and show that
they are consistent with previous findings. Finally, we outline the advantages
of using the Adomian Decomposition Method, which allows accurate solutions of
the S-N- system to be obtained quickly, even with minimal
computational resources.Comment: 20 pages, 1 table, 8 figure
Developing Clean Technology through Approximate Solutions of Mathematical Models
In this paper, the role of mathematical modeling in the development of clean technology has been considered.
One method each for obtaining approximate solutions of mathematical models by ordinary differential equations
and partial differential equations respectively arising from the modeling of systems and physical phenomena has
been considered. The construction of continuous hybrid methods for the numerical approximation of the solutions
of initial value problems of ordinary differential equations as well as homotopy analysis method, an approximate
analytical method, for the solution of nonlinear partial differential equations are discussed
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