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.
Research summary
Today, the Islamic nation is going through a phase that is one of the most dangerous that it has never experienced before. This phase was characterized by the following:
The nation is divided into states and its weakness in most of its doctrinal, political, social, economic and moral aspects.
Enemies targeting the nation's faith and capabilities, and the emergence of loyalty to the enemies of the nation from some groups of society, spreading misconceptions in the Muslim community.
Spreading the spirit of rebellion in all segments of society and striving to stir up the people against the rulers and put pressure on the rulers.
All these manifestations and others require the nation's wise men
... Show MoreThe research problem arose from the researchers’ sense of the importance of Digital Intelligence (DI), as it is a basic requirement to help students engage in the digital world and be disciplined in using technology and digital techniques, as students’ ideas are sufficiently susceptible to influence at this stage in light of modern technology. The research aims to determine the level of DI among university students using Artificial Intelligence (AI) techniques. To verify this, the researchers built a measure of DI. The measure in its final form consisted of (24) items distributed among (8) main skills, and the validity and reliability of the tool were confirmed. It was applied to a sample of 139 male and female students who were chosen
... Show MoreTopological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRS G2(4) indicating a simple undirected graph containing elements of G. Two distinct ertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.
Tobacco products of all kinds are harmful to public health, so legislation has paid great attention to regulating the process of tobacco production and distribution, whether at the level of national or international legislation, in a way that achieves legal protection for these products, so the establishment of civil liability for tobacco companies as a result of harm to the smoker The positive and the negative provoked a jurisprudential dispute due to the specificity of the work of these companies, and the jurisprudence differed in the legal nature of tobacco companies ’liability between contractual and tort liability in a way that enables the injured smoker to obtain his right to compensation.
Abstract
Friction stir welding is a relatively new joining process, which involves the joining of metals without fusion or filler materials. In this study, the effect of welding parameters on the mechanical properties of aluminum alloys AA2024-T351 joints produced by FSW was investigated.
Different ranges of welding parameters, as input factors, such as welding speed (6 - 34 mm/min) and rotational speed (725 - 1235 rpm) were used to obtain their influences on the main responses, in terms of elongation, tensile strength, and maximum bending force. Experimental measurements of main responses were taken and analyzed using DESIGN EXPERT 8 experimental design software which was used to develop t
... Show MoreReduction has been linked visually in art since man began making functional and aesthetic forms, and this beginning can be identified with cave paintings. Reduction is one of the clearest indications of intellectual presence in aesthetic experience. Modernism was greatly supported by the great transformations that the intellectual movement witnessed in the world in general and in Europe in particular. There, and their transfer of European artistic experiences, and the reflection of this influence in their aesthetic sculptures, and for this reason the researchers find that the study of the aesthetic references of the reductive forms in the Iraqi sculptural experience represents a great importance in the study of the history of contem
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