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.
A theoretical study on corrosion inhibitors was done by quantum calculations includes semi-empirical PM3 and Density Functional Theory (DFT) methods based on B3LYP/6311++G (2d,2P). Benzimidazole derivative (oxo(4- ((phenylcarbamothioyl) carbamoyl)phenyl) ammonio) oxonium (4NBP) and thiourea derivative 2-((4- bromobenzyl)thio) -1H-benzo[d] imidazole (2SB) were used as corrosion inhibitors and an essential quantum chemical parameters correlated with inhibition efficiency, EHOMO (highest occupied molecular orbital energy) and ELUMO (lowest molecular orbital energy). Other parameters are also studied like energy gap [ΔE (HOMO-LUMO)], electron affinity (EA), hardness (Δ), dipole moment (μ), softness (S), ionization potential (IE), absolut
... Show MoreThis research aims to know the essence of the correlative relationship between tactical thinking and solving mathematical problems. The researchers followed the descriptive research method to analyze relations, as all students from the mathematics department in the morning study were part of the research group. The research sample of (100) male and female students has been chosen based on the arbitrators' views. The tools for studying the sample of research composed of (12) items of the multiple-choice test in its final form to measure tactical thinking and require establish-ing a test of (6) test-type paragraphs to solve mathematical problems. The findings showed that sample students' tactical thinking and their capacity to overcome mathem
... Show MoreIn this research, the Iraqi flagpole at Baghdad University, which is the longest in Baghdad, with a height of 75m, was monitored. According to the importance of this structure, the calculation of the displacement (vertical deviation) in the structure was monitored using the Total Station device, where several observations were taken at different times for two years the monitoring started from November 2016 until May 2017, at a rate of four observations for one year. The observation was processed using the least square method, and the fitting of circles, and then the data was processed. The deviation was calculated using the Matlab program to calculate the values of corrections, where
Neuro-ophthalmology, bridging neurology and ophthalmology, highlights the nervous system’s crucial role in vision, encompassing afferent and efferent pathways. The evolution of this field has emphasized the importance of neuroanatomy for precise surgical interventions, presenting educational challenges in blending complex anatomical knowledge with surgical skills. This review examines the interplay between neuroanatomy and surgical practices in neuro-ophthalmology, aiming to identify educational gaps and suggest improvements.
A literature search across databases such as PubMed, Scopus, and W
Eye loss may be caused as a result of eye trauma, accidents, or malignant tumors, which leads the patient to undergo surgery to remove the damaged parts. This research examines the potential of computer vision represented by Structure from Motion (SfM) photogrammetry in fabricating the orbital prosthesis as a noninvasive and low-cost technique. A low-cost camera was used to collect the data towards extracting the dense 3D data of the patient facial features following Structure from Motion-Multi View Stereo (SfM-MVS) algorithms. To restore the defective orbital, a Reverse Engineering (RE) based approach has been applied using the similarity RE algorithms based on the opposite healthy eye to rehabilitate the defected orbital precisely
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In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit
... Show MoreBackground: The skull offers a high resistance of adverse environmental conditions over time, resulting in the greater stability of the dimorphic features as compared to other skeletal bony pieces. Sex determination of human skeletal considered an initial step in its identification. The present study is undertaken to evaluate the validity of 3D reconstructed computed tomographic images in sex differentiation by using craniometrical measurements at various parts of the skull. Materials and Method: 3D reconstructed computed tomographic scanning of 100 Iraqi subject, (50 males and 50 females) were analyzed with their age range from20-70 years old. Craniometrical linear measurements were located and marked on both side of the 3D skull images.
... Show MoreNecessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.