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This paper provides a new proof of the existence and uniqueness of the solution for a nonlinear boundary value problem (1+δy)y′′+2x(1+γy)y′=0,0

The general form of explicit, analytical solution of the Frost-Kalkwarf equation was developed for the first time by means of the Adomian decomposition method as a reliable mathematical tool. The accuracy of the obtained formulas was further improved by applying the diagonal Padé approximants. We have demonstrated that our developed formulas are at least 30 times faster than the original Frost-Kalkwarf equation in computation of vapour pressures and are highly accurate with an overall absolute relative deviation of 2.25 % for 88 different substances over 26 400 experimental data points from triple to critical point temperatures. As another unique advantage, our formulas avoid any divergent behaviour in using iterative methods unlike the implicit Frost-Kalkwarf equation. Based on the conducted statistical analyses, our formulas have excellent predictability of vapour pressure values with a probability of 90.33 % for absolute relative errors of less than 5 %. [ABSTRACT FROM AUTHOR]

A number of control schemes including nonlinear feedback, dislocated feedback, and speed feedback have been proposed and assessed for a bromate-malonic acid-cerium Belousov-Zhabotinsky batch reaction process. The tuning parameters of the Oregonator model were firstly adjusted based on a UV-vis spectrophotometric analysis in the experimental part of the research. The adjusted Oregonator model successfully reproduced the innate induction time and periodicity of the BZ-batch system. Subsequently, the controllers were implemented and numerical simulations were carried out by employing the multi-stage Adomian decomposition method. The nominal analysis method was used to study the linear stability of each design. All the controlled systems were found to be linearly stable for certain continuous regions of controller gain. The performance of the proposed control laws was assessed and the dislocated feedback control strategy was shown to be able to drive the system states toward desired setpoints quickly. Furthermore, the validity of the dislocated feedback control design was doubly ensured by the sliding mode control theory. It was found that those feedback schemes which manipulate cerium ion concentration can be practically realized by means of electrochemical oxidation or oxygen aeration. Our results were confirmed by the Simulink software package and the block diagram representations are included in the paper. [ABSTRACT FROM AUTHOR]

The Hall-Yarborough equation (H-Y equation) of state has been favoured in natural gas engineering due to its accuracy and conciseness for many years. In this paper, the Adomian decomposition method (ADM) is employed to devise a novel algorithm for calculating the compressibility factors of natural gases through this reliable equation of state. A convergence accelerator technique, namely the efficient Shanks transform, is also exploited to further improve our scheme in terms of computational speed. Unlike most of the previous numerical solution strategies, our algorithm does not require an initial guess as the starting point and is computationally efficient. The proposed algorithm is found to be superior over the common Newton-Raphson algorithm, where we have also demonstrated that the latter can easily lead to grossly erroneous solutions. For the sake of illustration, a number of real-world case study problems are solved by our algorithm and relevant comparisons are provided. [ABSTRACT FROM AUTHOR]

In this paper, we introduce systems of Volterra integral forms of the Lane-Emden equations. We use the systematic Adomian decomposition method to handle these systems of integral forms. The Volterra integral forms overcome the singular behavior at the origin x = 0. The Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. Our results are supported by investigating several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a new approach to calculate analytic approximations of blow-up solutions and their critical blow-up times. Our approach applies the Adomian decomposition-Padé method to quickly and easily compute the critical blow-up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]