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88 articles for “Iteration”
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Research ArticleOpen accessEvery word in the titlePerturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model EquationsGrace O. Akinlabi, Sunday O. EdekiIn this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead-Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 20 Feb 2017 · 6,987 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleLOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITHIN LOCAL FRACTIONAL OPERATORSAmmar Ali NeamahThe paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations. …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 9 Oct 2014 · 6,511 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration MethodS.S. Nourazar, A. Nazari-Golshan, M. NourazarProblem statement: In the present study, a hybrid of Fourier transform and Variational Iteration Method (FTVIM) is developed for solving the non-homogeneous linear and nonlinear partial differential equations of Cauchy reaction-diffusion problem. Approach: The closed form solutions obtained from the series solution of recursive sequences is valid for the entire range of problem domain. Results and Conclusion: Moreover, the very … …Physics International, Vol. 2, Issue 1 · 26 Oct 2011 · 8,195 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleNumerical Solutions of the Multispecies Predator-Prey Model by Variational Iteration MethodKhaled BatihaThe main objective of the current work was to solve the multispecies predator-prey model. The techniques used here were called the variational iteration method (VIM) and the Adomian decomposition method (ADM). The advantage of this work is twofold. Firstly, the VIM reduces the computational work. Secondly, in comparison with existing techniques, the VIM is an improvement with regard to its … …Journal of Computer Science, Vol. 3, Issue 7 · 31 Jul 2007 · 6,793 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleApproximate Analytical Solutions For Time-Dependent Emden-Fowler-Type Equations By Variational Iteration MethodKhaled BatihaThe main objective of the current study was to solve the time-dependent Emden-Fowler-type equation with singular behavior. The technique used here was called the variational iteration method (VIM). The advantage of this work is twofold. Firstly, the VIM reduces the computational work. Secondly, in comparison with existing techniques, the VIM is an improvement with regard to its accuracy and rapid … …American Journal of Applied Sciences, Vol. 4, Issue 7 · 31 Jul 2007 · 6,591 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleSome Stability Results on Krasnolslseskij and Ishikawa Fixed Point Iteration ProceduresM. O. Olatinwo, O. O. Owojori, C. O. ImoruIn this study, we establish some stability results for the Krasnoselskij and the Ishikawa iteration procedures. We employ the same method as in Berinde[1], but using a more general contractive definition than those of Berinde[1], Rhoades[2], Harder and Hicks[3] and Osilike[4,5]. …Journal of Mathematics and Statistics, Vol. 2, Issue 1 · 31 Mar 2006 · 6,935 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Some Stability Results for Fixed Point Iteration ProcedureM. O. Olatinwo, O. O. Owojori, C. O. ImoruIn this study, we establish that both the Mann and Ishikawa iteration processes are T-stable for the mappings T satisfying a more general contractive definition than that of Osilike[1] . The results obtained generalize some of the recent results of Osilike[1] which are themselves generalizations and extensions of some of the results of Harder and Hicks[2] and Rhoades[3,4]. …Journal of Mathematics and Statistics, Vol. 2, Issue 1 · 31 Mar 2006 · 7,040 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleApproximation of Iteration Number for Gauss-Seidel Using Redlich-Kister PolynomialM. K. Hasan, J. Sulaiman, S. Ahmad et al.Problem statement: Development of mathematical models based on set of observed data plays a crucial role to describe and predict any phenomena in science, engineering and economics. Therefore, the main purpose of this study was to compare the efficiency of Arithmetic Mean (AM), Geometric Mean (GM) and Explicit Group (EG) iterative methods to solve system of linear equations via estimation … …American Journal of Applied Sciences, Vol. 7, Issue 7 · 31 Jul 2010 · 8,138 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleHomotopy Perturbation Method and Variational Iteration Method for Solving Zakharov-Kuznetsov EquationB. Ganjavi, H. Mohammadi, D.D. Ganji, A. BarariThis article investigates a nonlinear dispersive Zakharov-Kuznetsov ZK (3, 3, 3) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) are implemented for solving the ZK equation. Homotopy results were compared with … …American Journal of Applied Sciences, Vol. 5, Issue 7 · 31 Jul 2008 · 6,798 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleModified Hill Cipher for a Large Block of Plaintext with Interlacing and IterationV. U.K. Sastry, N. R. ShankarIn this research, we have developed a large block cipher by modifying the Hill cipher. In this, we have introduced interlacing of the binary bits of the plaintext as the primary concept leading to confusion. This process is strengthened by using iteration. The cryptanalysis and avalanche effect mentioned in this research clearly exhibit the strength of the cipher. …Journal of Computer Science, Vol. 4, Issue 1 · 31 Jan 2008 · 7,150 accessesView PDFCite