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.
MT Suhail, SA Hussein, MN Abdulhussein, WQ Abdaullateef, M khairallah Aid…, Migration Letters, 2024
This study assesses the short-term and long-term interactions between firm performance, financial education and political instability in the case of Malaysia Small to Medium Enterprises (SMEs). The simultaneous insertion of financial education and political instability within the study is done intentionally to inspect the effect of these two elements in one equation for the Malaysian economy. Using the bound testing methodology for cointegration and error correction models, advanced within an autoregressive distributed lag (ARDL) framework, we examine whether a long-run equilibrium connection survives between firm performance and the above mentioned independent variables. Using this method, we uncover evidence of a positive long-term link b
... Show MoreZnS:MnP2+P nanoparticles were prepared by a simple microwave irradiation method under mild condition. The starting materials for the synthesis of ZnS:MnP 2+P quantum dots were zinc acetate as zinc source, thioacetamide as a sulfur source, manganese chloride as manganese source (R & M Chemical) and ethylene glycol as a solvent. All chemicals were analytical grade products and used without further purification. The quantum dots of ZnS:MnP 2+P with cubic structure were characterized by X-ray powder diffraction (XRD), the morphology of the film is seen by scanning electron microscopy (SEM) also by field effect scanning electron microscopy (FESEM). The composition of the samples is analysed by EDS. UV-Visible absorption spectroscopy analysis
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<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability
... Show MoreIn this research, Argon gas was used to generate atmospheric plasma in the manufacture of platinum nanomaterials, to study the resultant plasma spectrum and to calculate the cellular toxicity of those manufactured nanomaterials. This research is keen on the generation of nonthermal atmospheric pressure plasma using aqueous platinum salts (H2PtCl6 6H2O) with different concentrations and exposure of cold plasma with a different time period used to produce platinum nanoparticles, to ensure typical preparation of nanoparticles. Visible UV and X-rays were performed for this purpose, and the diameter of the system probe was (1[Formula: see text]mm) with the Argon gas flow of
... Show MoreThis study aims to identify the forgiveness level among gifted students and its relation to the self-awareness. The study sample consisted of (207) students were randomly chosen, they are integrated in secondary schools in Abha / Saudi Arabia. The correlative, analytical descriptive method was adopted. Two scales were adopted by the researcher: The forgiveness scale prepared by Rye et al (2001) which translated to Arabic by Al-Mahasneh (2017) and the self-awareness scale which prepared by Al-Ghezwani (2017). The study results indicated the following: the forgiveness level among the talented students was high, the self-awareness level among talented students was high, and there is a positive statistically significant relationship
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