In the present paper, three reliable iterative methods are given and implemented to solve the 1D, 2D and 3D Fisher’s equation. Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM) and Banach contraction method (BCM) are applied to get the exact and numerical solutions for Fisher's equations. The reliable iterative methods are characterized by many advantages, such as being free of derivatives, overcoming the difficulty arising when calculating the Adomian polynomial boundaries to deal with nonlinear terms in the Adomian decomposition method (ADM), does not request to calculate Lagrange multiplier as in the Variational iteration method (VIM) and there is no need to create a homotopy like in the Homotopy perturbation method (HPM), or any assumptions to deal with the nonlinear term. The obtained solutions are in recursive sequence forms which can be used to achieve the closed or approximate form of the solutions. Also, the fixed point theorem was presented to assess the convergence of the proposed methods. Several examples of 1D, 2D and 3D problems are solved either analytically or numerically, where the efficiency of the numerical solution has been verified by evaluating the absolute error and the maximum error remainder to show the accuracy and efficiency of the proposed methods. The results reveal that the proposed iterative methods are effective, reliable, time saver and applicable for solving the problems and can be proposed to solve other nonlinear problems. All the iterative process in this work implemented in MATHEMATICA®12. ABSTRAK: Kajian ini berkenaan tiga kaedah berulang boleh percaya diberikan dan dilaksanakan bagi menyelesaikan 1D, 2D dan 3D persamaan Fisher. Kaedah Daftardar-Jafari (DJM), kaedah Temimi-Ansari (TAM) dan kaedah pengecutan Banach (BCM) digunakan bagi mendapatkan penyelesaian numerik dan tepat bagi persamaan Fisher. Kaedah berulang boleh percaya di kategorikan dengan pelbagai faedah, seperti bebas daripada terbitan, mengatasi masalah-masalah yang timbul apabila sempadan polinomial bagi mengurus kata tak linear dalam kaedah penguraian Adomian (ADM), tidak memerlukan kiraan pekali Lagrange sebagai kaedah berulang Variasi (VIM) dan tidak perlu bagi membuat homotopi sebagaimana dalam kaedah gangguan Homotopi (HPM), atau mana-mana anggapan bagi mengurus kata tak linear. Penyelesaian yang didapati dalam bentuk urutan berulang di mana ianya boleh digunakan bagi mencapai penyelesaian tepat atau hampiran. Juga, teorem titik tetap dibentangkan bagi menaksir kaedah bentuk hampiran. Pelbagai contoh seperti masalah 1D, 2D dan 3D diselesaikan samada secara analitik atau numerik, di mana kecekapan penyelesaian numerik telah ditentu sahkan dengan menilai ralat mutlak dan baki ralat maksimum (MER) bagi menentukan ketepatan dan kecekapan kaedah yang dicadangkan. Dapatan kajian menunjukkan kaedah berulang yang dicadangkan adalah berkesan, boleh percaya, jimat masa dan boleh guna bagi menyelesaikan masalah dan boleh dicadangkan menyelesaikan masalah tak linear lain. Semua proses berulang dalam kerja ini menggunakan MATHEMATICA®12.
In this paper the research represents an attempt of expansion in using the parametric and non-parametric estimators to estimate the median effective dose ( ED50 ) in the quintal bioassay and comparing between these methods . We have Chosen three estimators for Comparison. The first estimator is
( Spearman-Karber ) and the second estimator is ( Moving Average ) and The Third estimator is ( Extreme Effective Dose ) . We used a minimize Chi-square as a parametric method. We made a Comparison for these estimators by calculating the mean square error of (ED50) for each one of them and comparing it with the optimal the mean square
Four rapid, accurate and very simple derivative spectrophotometric techniques were developed for the quantitative determination of binary mixtures of estradiol (E2) and progesterone (PRG) formulated as a capsule. Method I is the first derivative zero-crossing technique, derivative amplitudes were detected at the zero-crossing wavelength of 239.27 and 292.51 nm for the quantification of estradiol and 249.19 nm for Progesterone. Method II is ratio subtraction, progesterone was determined at λmax 240 nm after subtraction of interference exerted by estradiol. Method III is modified amplitude subtraction, which was established using derivative spectroscopy and mathematical manipulations. Method IIII is the absorbance ratio technique, absorba
... Show MoreThe importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It pro
... Show MoreDescribed the Arabic language being of genius sets by top models of eloquence , rhetoric and clarity of sounds and developments Moreover , it is an important element of our existence and our identity and our survival . That my methods and best in teaching Arabic language what has pursued the easiest ways to learning and teaching and helped learners to be aware of the function linguistic information , and they need it and its impact on their lives , and contributed to unleashing the potential of activism and led them to make the effort to apply them in the form of examples and uses of new life , as well as fits are the capabilities and tendencies of different learners , so the goal of current research into the importance of the curriculum
... Show MoreThe banking system considered as one of the most important intermediate circle between creditor and debtors it is mean the most important funding rings in economic activity, whether finance takes the a consumer or investment form and therefore it is the main base to stimulate economic activity both on the demand side, both consumption and investment and therefore of the main motivating factors for economic growth.
The banking system depends in achieve its goals on the grants and loan recovery, or what is known credit process and according to what the importance referred to the role of the banking system, it is important to ensure the safety and efficiency of the mechanisms of banking device and safety is
... Show Morethe rationalization of energy consumption Require awareness in the possibility of bridging the local need severe shortage of electric power for daily requirements. The research aims to show that the engineers of various specializations and architects, including in particular can have an active role in about the importance of the role of energy in human life, and it’s best utilization without extravagance (which our religion forbids it). Here lies the problem of the research to find possible means and alternative methods to reduce (rationalization) electrical energy consumption in hot dry areas in general which need large energy for air conditioning because of the crucial climate of these regions that making access to the area o
... Show MoreHartree-Fock (HF) method relies in the calculations of nonlinear optical properties (NLO) for benzoic acid molecule. Also, another theoretical study is conducted by using the TD-DFT Density Functional Theory through B3LYP/High Base Set 6-311++G (2d,2p) on Gaussian program09. Moreover, an experimental study has been done to obtain the electrons spectrum for benzoic acid with and without ethanol. While the experimental study is done by using UV/VIS. spectrophotometer. Energy gap values of electronic transition between HOMO and LUMO is obtained from theoretical and experimental results. Consequently, the theoretical result for determining the energy gap calculated from EHOMO-LUMO wasvery close to the results of UV / VIS. spectrum. A theoretica
... Show MoreA substantial portion of today’s multimedia data exists in the form of unstructured text. However, the unstructured nature of text poses a significant task in meeting users’ information requirements. Text classification (TC) has been extensively employed in text mining to facilitate multimedia data processing. However, accurately categorizing texts becomes challenging due to the increasing presence of non-informative features within the corpus. Several reviews on TC, encompassing various feature selection (FS) approaches to eliminate non-informative features, have been previously published. However, these reviews do not adequately cover the recently explored approaches to TC problem-solving utilizing FS, such as optimization techniques.
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