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, we have been used the Hermite interpolation method to solve second order regular boundary value problems for singular ordinary differential equations. The suggest method applied after divided the domain into many subdomains then used Hermite interpolation on each subdomain, the solution of the equation is equal to summation of the solution in each subdomain. Finally, we gave many examples to illustrate the suggested method and its efficiency.
The attribute quality control charts are one of the main useful tools to use in control of quality product in companies. In this paper utilizing the statistical procedures to find the attribute quality control charts for through fuzzified the real data which we got it from Baghdad Soft Drink Company in Iraq, by using triangular membership function to obtain the fuzzy numbers then employing the proposed ranking function to transform to traditional sample. Then, compare between crisp and fuzzy attribute quality control.
While analytical solutions to Quadratic Assignment Problems (QAP) have indeed been since a long time, the expanding use of Evolutionary Algorithms (EAs) for similar issues gives a framework for dealing with QAP with an extraordinarily broad scope. The study's key contribution is that it normalizes all of the criteria into a single scale, regardless of their measurement systems or the requirements of minimum or maximum, relieving the researchers of the exhaustively quantifying the quality criteria. A tabu search algorithm for quadratic assignment problems (TSQAP) is proposed, which combines the limitations of tabu search with a discrete assignment problem. The effectiveness of the proposed technique has been compared to well-established a
... Show MoreThat achieve a level of excellence for the quality of university education cannot be achieved only by uniting the efforts of all employees at the university and active participation by students and by alumni and the labor market and society, however we can say that the administrative and academic university staff play an active role and the largest in achieving equivalent quality of higher education, It should unite the efforts of all employees in the educational institution in order to achieve quality education. It is the concept of quality of education, quality assurance and overall management of the quality of the basic pillars on which it is based university education. That highlight the need fo
... Show MoreA simulation study is used to examine the robustness of some estimators on a multiple linear regression model with problems of multicollinearity and non-normal errors, the Ordinary least Squares (LS) ,Ridge Regression, Ridge Least Absolute Value (RLAV), Weighted Ridge (WRID), MM and a robust ridge regression estimator MM estimator, which denoted as RMM this is the modification of the Ridge regression by incorporating robust MM estimator . finialy, we show that RMM is the best among the other estimators
In this review, numerous analytical methods to distinguish pigments in tattoo, paint, and ink items are discussed. The selection of a method was dependent upon the purpose, e.g., quantification or identification of pigments. The introductory part of this review focuses on describing the importance of setting up a pigment-associated safety profile. The formation of different degradation chemical substances as well as impurity trends can be indicated through the chemical investigation of pigments in tattoo products. It is noteworthy that pigment recognition in tattoo inks can work as a preliminary method to identify the pigments in a patient's tattoo before being removed by laser therapy. Contrary to the stud
Two simple and sensitive spectrophotometric methods are proposed for the determination of amitriptyline in its pure form and in tablets. The first method is based on the formation of charge- transfer complex between amitriptyline as n-donor and tetracyano-ethylene (TCNE) as πacceptor. The product exhibit absorbance maximum at 470 nm in acetonitrile solvent (pH =9.0 ) . In the second method the absorbance of the ion- pair complex, which is formed between the soughted drug and bromocresol green (BCG), was measured at 415 nm at ( pH=3.5) . In addition to classical univariate optimization, modified simplex method (MSM) was applied in the optimization of the variable affecting the color producing reaction by a geometric simple
... Show MoreIn this review, numerous analytical methods to distinguish pigments in tattoo, paint, and ink items are discussed. The selection of a method was dependent upon the purpose, e.g., quantification or identification of pigments. The introductory part of this review focuses on describing the importance of setting up a pigment-associated safety profile. The formation of different degradation chemical substances as well as impurity trends can be indicated through the chemical investigation of pigments in tattoo products. It is noteworthy that pigment recognition in tattoo inks can work as a preliminary method to identify the pigments in a patient's tattoo before being removed by laser therapy. Contrary to the stud
Stereolithography (SLA) has become an essential photocuring 3D printing process for producing parts of complex shapes from photosensitive resin exposed to UV light. The selection of the best printing parameters for good accuracy and surface quality can be further complicated by the geometric complexity of the models. This work introduces multiobjective optimization of SLA printing of 3D dental bridges based on simple CAD objects. The effect of the best combination of a low-cost resin 3D printer’s machine parameter settings, namely normal exposure time, bottom exposure time and bottom layers for less dimensional deviation and surface roughness, was studied. A multiobjective optimization method was utilized, combining the Taguchi me
... Show MoreWhen scheduling rules become incapable to tackle the presence of a variety of unexpected disruptions frequently occurred in manufacturing systems, it is necessary to develop a reactive schedule which can absorb the effects of such disruptions. Such responding requires efficient strategies, policies, and methods to controlling production & maintaining high shop performance. This can be achieved through rescheduling task which defined as an essential operating function to efficiently tackle and response to uncertainties and unexpected events. The framework proposed in this study consists of rescheduling approaches, strategies, policies, and techniques, which represents a guideline for most manufacturing companies operatin
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