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Direct solutions of N-th order initial value problems in decomposition series
(Freund Publishing House Ltd, 2007)
Yahaya F.
;
Hashim I.
;
Ismail E.S.
;
Zulkifle A.K.
;
36933055900
;
10043682500
;
10045432900
;
7801341335
In this paper, a class of linear and non-linear nth-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by adapting the modified Adomian decomposition method (MADM) as an algorithm for approximating the solutions of the equations in a sequence of time intervals (i.e. time steps). In this way the series solutions are valid for quite a long time span. Several test cases are chosen to demonstrate the performance of the multistage modified Adomian decomposition method (MMADM). �Freund Publishing House Ltd.
Dynamics of the Hantavirus infection through variational iteration method
(2009)
Goh S.M.
;
Ismail A.I.M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
27172423000
;
6603683028
;
10043682500
This paper studies the dynamics of the Hantavirus infection model, which was originally developed by Abramson and Kenkre [G. Abramson, V.M. Kenkre, Spatiotemporal patterns in the hantavirus infection, Phys. Rev. E 66 (2002) 011912], by using a simple analytical method called the variational iteration method or VIM. The results obtained by the variational iteration method are compared with the classical Runge-Kutta method (fourth-order) to gauge its effectiveness. Numerical values from these analyses provide us with some useful observation on the behaviour of the infection subjected to certain conditions. � 2008 Elsevier Ltd. All rights reserved.
Effect of finite wall thickness on entropy generation and natural convection in a nanofluid-filled partially heated square cavity
(Emerald Publishing, 2020)
Ishak M.S.
;
Alsabery A.I.
;
Chamkha A.
;
Hashim I.
;
57208024651
;
56705372300
;
35568909100
;
10043682500
Purpose: The purpose of this paper is to study the effects of finite wall thickness on the natural convection and entropy generation in a square cavity filled with Al2O3�water nanofluid in the presence of bottom heat source. Design/methodology/approach: The moving isothermal heater was placed on the bottom solid wall. The vertical walls (left and right walls) were fully maintained at low temperatures. The rest of the bottom solid wall along with the top horizontal wall was kept adiabatic. The boundaries of the domain are assumed to be impermeable; the fluid within the cavity is a water-based nanofluid having Al2O3 nanoparticles. The Boussinesq approximation is applicable. The dimensionless governing equations subject to the selected boundary conditions are solved using the finite difference method. The current proposed numerical method is proven excellent through comparisons with the existing experimental and numerical published studies. Findings: Numerical results were demonstrated graphically in several forms including streamlines, isotherms and local entropy generation, as well as the local and average Nusselt numbers. The results reveal that the thermal conductivity and thickness of the solid wall are important control parameters for optimization of heat transfer and Bejan number within the partially heated square cavity. Originality/value: According to the past research studies mentioned above and to the best of the authors� knowledge, the gap regarding the problem with entropy generation analysis and natural convection in partially heated square cavity has yet to be filled. Because of this, this study aims to investigate the entropy generation analysis as well as the natural convection in nanofluid-filled square cavity which was heated partially. A square cavity with an isothermal heater located on the bottom solid horizontal wall of the cavity and partly cold sidewalls are essential problems in thermal processing applications. Hence, the authors believe that this present work will be a valuable contribution in improving the thermal performance. � 2019, Emerald Publishing Limited.
Efficacy of variational iteration method for chaotic Genesio system - Classical and multistage approach
(Elsevier Ltd, 2009)
Goh S.M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
6603683028
;
10043682500
This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work. � 2007 Elsevier Ltd. All rights reserved.
Enhanced variational iteration method using adomian polynomials for solving the chaotic lorenz system
(Walter de Gruyter GmbH, 2010)
Goh S.M.
;
Mossa Al-Sawalha M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
55664495900
;
6603683028
;
10043682500
A merger of two numeric-analytic methods poses various challenges, but also holds promise. Such a fusion could enhance the performance of calculations and may also overcome certain drawbacks of each used individually. This paper focuses on solving the chaotic Lorenz system, a three-dimensional system of ordinary differential equations with quadratic nonlinearities, using a newly designed hybrid algorithm merging multistage variational iteration method with Adomian polynomials. The core of this algorithm is made by surrogating the nonlinear terms in the variational iteration method with Adomian polynomials. Numerical comparisons are made between the hybrid and the classic fourth-order Runge-Kutta method. Our work demonstrates that the multistage hybrid provides good accuracy and efficiency for the chaotic Lorenz system. �Freund Publishing House Ltd.
Entropy generation analysis and natural convection in a nanofluid-filled square cavity with a concentric solid insert and different temperature distributions
(MDPI AG, 2018)
Alsabery A.I.
;
Ishak M.S.
;
Chamkha A.J.
;
Hashim I.
;
56705372300
;
57208024651
;
35568909100
;
10043682500
The problem of entropy generation analysis and natural convection in a nanofluid square cavity with a concentric solid insert and different temperature distributions is studied numerically by the finite difference method. An isothermal heater is placed on the bottom wall while isothermal cold sources are distributed along the top and side walls of the square cavity. The remainder of these walls are kept adiabatic. Water-based nanofluids with Al2O3 nanoparticles are chosen for the investigation. The governing dimensionless parameters of this study are the nanoparticles volume fraction (0 ? ? ? 0.09), Rayleigh number (103 ? Ra ? 106), thermal conductivity ratio (0.44 ? Kr ? 23.8) and length of the inner solid (0 ? D ? 0.7). Comparisons with previously experimental and numerical published works verify a very good agreement with the proposed numerical method. Numerical results are presented graphically in the form of streamlines, isotherms and local entropy generation as well as the local and average Nusselt numbers. The obtained results indicate that the thermal conductivity ratio and the inner solid size are excellent control parameters for an optimization of heat transfer and Bejan number within the fully heated and partially cooled square cavity. � 2018 by the authors.
Entropy generation and natural convection of nanofluids in a trapezoidal cavity having an innersolid cylinder
(IOP Publishing Ltd, 2021)
Ishak M.S.
;
Alsabery A.I.
;
Hashim I.
;
57208024651
;
56705372300
;
10043682500
A numerical analysis of entropy generation and natural convection in a trapezoidal cavity with an internal solid cylinder filled with Al2O3 - water nanofluid has been investigated using finite difference method. The bottom wall is thermally insulated while the left and right walls were cooled isothermally. Remainder of these walls are kept adiabatic. Particular factors have been focused on the effects of Rayleigh number, dimensionless radius of the solid cylinder and nanoparticles of volume fraction on streamlines, isotherms, isentropic, local and average Nusselt number. Obtained results have demonstrated that the Rayleigh number and size of the solid cylinder are important control parameters for optimizing heat transfer and Bejan number. � Published under licence by IOP Publishing Ltd.
Entropy production and mixed convection within trapezoidal cavity having nanofluids and localised solid cylinder
(Nature Research, 2021)
Ishak M.S.
;
Alsabery A.I.
;
Hashim I.
;
Chamkha A.J.
;
57208024651
;
56705372300
;
10043682500
;
35568909100
The entropy production and mixed convection within a trapezoidal nanofluid-filled cavity having a localised solid cylinder is numerically examined using the finite element technique. The top horizontal surface moving at a uniform velocity is kept at a cold temperature, while the bottom horizontal surface is thermally activated. The remaining surfaces are maintained adiabatic. Water-based nanofluids (Al 2O 3 nanoparticles) are used in this study, and the Boussinesq approximation applies. The influence of the Reynolds number, Richardson number, nanoparticles volume fraction, dimensionless radius and location of the solid cylinder on the streamlines, isotherms and isentropic are examined. The results show that the solid cylinder�s size and location are significant control parameters for optimising the heat transfer and the Bejan number inside the trapezoidal cavity. Furthermore, the maximum average Nusselt numbers are obtained for high R values, where the average Nusselt number is increased by 30% when R is raised from 0 to 0.25. � 2021, The Author(s).
Introducing variational iteration method to a biochemical reaction model
(2010)
Goh S.M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
6603683028
;
10043682500
A basic enzyme kinetics is used to test the effectiveness of an analytical method, called the variational iteration method (VIM). This enzymesubstrate reaction is formed by a system of nonlinear ordinary differential equations. We shall compare the classical VIM against a modified version called the multistage VIM (MVIM). Additional comparison will be made against the conventional numerical method, RungeKutta (RK4)(fourth-order). Numerical results were obtained for these three methods and we found that MVIM and RK4 are in excellent conformance. � 2009 Elsevier Ltd. All rights reserved.
A new application of variational iteration method for the chaotic R�ssler system
(Elsevier Ltd, 2009)
Goh S.M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
6603683028
;
10043682500
This paper emphasizes the strength of variational iteration method (VIM) in numerically solving the chaotic R�ssler system. The R�ssler system is a three-dimensional system of ODEs with quadratic nonlinearities. An adaptation of the VIM was implemented and is called the multistage VIM (MVIM). Numerical comparisons are made between MVIM and the classical fourth-order Runge-Kutta (RK4) with results showing extremely good performance by MVIM, yielding great accuracy and efficiency. � 2009 Elsevier Ltd. All rights reserved.
On solving the chaotic Chen system: A new time marching design for the variational iteration method using Adomian's polynomial
(2010)
Goh S.M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
6603683028
;
10043682500
This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving the chaotic Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This research implements the multistage variational iteration method with an emphasis on the new multistage hybrid of variational iteration method with Adomian polynomials. Numerical comparisons are made between the multistage variational iteration method, the multistage variational iteration method using the Adomian's polynomials and the classic fourth-order Runge-Kutta method. Our work shows that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage variational iteration method. � 2009 Springer Science+Business Media, LLC.
Prescribing a multistage analytical method to a prey-predator dynamical system
(Elsevier, 2008)
Goh S.M.
;
Noorani M.S.M.
;
Hashim I.
;
25521891600
;
6603683028
;
10043682500
This article discusses the effectiveness of a fresh analytical method in solving a prey-predator problem, which is described as a system of two nonlinear ordinary differential equations. The method of interest is the multistage variational iteration method (MVIM), which provides a slight modification of the classical variational iteration method (VIM). We shall compare solutions of the classical VIM along with MVIM and match them against the conventional numerical method, Runge-Kutta (RK4) (fourth-order). � 2008.
Variational iteration method as a reliable treatment for the hyperchaotic r�ssler system
(Freund Publishing House Ltd, 2009)
Goh S.M.
;
Noorani M.S.N.
;
Hashim I.
;
Al-Sawalha M.M.
;
25521891600
;
6603683028
;
10043682500
;
55664495900
This paper concerns the implementation of variational iteration method (VIM) in solving the hyperchaotic R�ssler analytically. It is a four dimensional system of ODEs with quadratic nonlinearities. The computation was made using a newly found version called the multistage VIM (MVIM) which offers some slight modification to the traditional VIM. Numerical comparisons are made between MVIM and the classical fourth-order Runge-Kutta (RK4) with results displaying extremely good performance by MVIM, yielding great accuracy and efficiency. It is also evident that MVIM surpasses (in terms of accuracy) its two counterparts, the Adomian decomposition method (ADM) and Differential transformation method (DTM).

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