O. González-Gaxiola, A. Biswas, Y. Yıldırım, A. Alshomrani
This paper is a numerical study of the bright optical solitons that emerge from the concatenation model which is considered with power-law nonlinearity. The Laplace-Adomian decomposition scheme is the integration methodology adopted in the paper. The surface plots are exhibited for a range of values of the power-law parameter.
{"title":"Bright Optical Solitons for the Concatenation Model with Power-Law Nonlinearity: Laplace-Adomian Decomposition","authors":"O. González-Gaxiola, A. Biswas, Y. Yıldırım, A. Alshomrani","doi":"10.37256/cm.4420233705","DOIUrl":"https://doi.org/10.37256/cm.4420233705","url":null,"abstract":"This paper is a numerical study of the bright optical solitons that emerge from the concatenation model which is considered with power-law nonlinearity. The Laplace-Adomian decomposition scheme is the integration methodology adopted in the paper. The surface plots are exhibited for a range of values of the power-law parameter.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"51 7","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138976817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is to characterize isometries of multiplication operators and weighted composition operators on the nth weighted-type Banach spaces {Vn : n ∈ N} of analytic functions on the open unit disk of which the Bloch space and the Zygmund space are particular cases at n = 1, 2. We give characterizations of the symbols ψ and φ for which the multiplication operator Mψ and the weighted composition operator Wψ,φ are surjective isometries. Moreover, we show that generalized weighted composition operators are not isometric on Vn.
{"title":"Surjective Isometries of Multiplication Operators and Weighted Composition Operators on nth Weighted-Type Banach Spaces of Analytic Functions","authors":"Shams Alyusof","doi":"10.37256/cm.4420232472","DOIUrl":"https://doi.org/10.37256/cm.4420232472","url":null,"abstract":"\u0000\u0000\u0000This paper is to characterize isometries of multiplication operators and weighted composition operators on the nth weighted-type Banach spaces {Vn : n ∈ N} of analytic functions on the open unit disk of which the Bloch space and the Zygmund space are particular cases at n = 1, 2. We give characterizations of the symbols ψ and φ for which the multiplication operator Mψ and the weighted composition operator Wψ,φ are surjective isometries. Moreover, we show that generalized weighted composition operators are not isometric on Vn.\u0000\u0000\u0000","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"9 8","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139007609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Bhat, H. A. Rizvi, J. Ganie, Faiza A. Sulaiman, D. K. Jain
In this paper, Volterra q-integral equations are solved by using the method of q-differential transformation. Exact solutions of linear and nonlinear q-integral equations have been investigated. To illustrate the method, several problems are discussed for the effectiveness and performance of the proposed method.
{"title":"Differential Transform Method for Solving Volterra q-Integral Equations","authors":"A. Bhat, H. A. Rizvi, J. Ganie, Faiza A. Sulaiman, D. K. Jain","doi":"10.37256/cm.4420232549","DOIUrl":"https://doi.org/10.37256/cm.4420232549","url":null,"abstract":"In this paper, Volterra q-integral equations are solved by using the method of q-differential transformation. Exact solutions of linear and nonlinear q-integral equations have been investigated. To illustrate the method, several problems are discussed for the effectiveness and performance of the proposed method.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"14 11","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139008679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The preservation of sensitive data and prevention of unauthorized access are critical objectives in cloud computing environments, necessitating the implementation of robust security measures. The present study delves into the amalgamation of the Hierarchical Role Based Access Control Model (HR-ACM), Composikey, a composite key encryption algorithm, and Interactive Tree Based zero knowledge protocol (ITZKP) to construct a robust security framework for cloud security. This study presents an investigation into the viability and efficacy of integrating HRACM, Composikey, and ITZKP as a means of augmenting security measures and reducing potential hazards in cloudbased systems. The execution times comparison of the Composikey, IBPRE, and KPRE models were compared for different filesizes (1 KB to 2 GB) to evaluate the performance of the HRACM method. As roles increase, RBAC a execution time increases significantly. The HRACM Method takes 0.001 to 0.002 seconds to implement across all role counts. The results show that the HRACM Method is more efficient and time-effective than the RBAC Method. The response time measured in microseconds for the existing ZKP and Libra systems for different file sizes, ranging from 1KB to 1 GB. The results reveal that the verifier time for the ITZKP system aligns closely with the existing systems, demonstrating its ability to perform efficient verification processes. These findings collectively demonstrate the potential of the integrated security framework in enhancing cloud security.
{"title":"Identity and Access Control Techniques for Enhanced Data Communication in Cloud","authors":"Rashmi Dixit, K. Ravindranath","doi":"10.37256/cm.5120243721","DOIUrl":"https://doi.org/10.37256/cm.5120243721","url":null,"abstract":"The preservation of sensitive data and prevention of unauthorized access are critical objectives in cloud computing environments, necessitating the implementation of robust security measures. The present study delves into the amalgamation of the Hierarchical Role Based Access Control Model (HR-ACM), Composikey, a composite key encryption algorithm, and Interactive Tree Based zero knowledge protocol (ITZKP) to construct a robust security framework for cloud security. This study presents an investigation into the viability and efficacy of integrating HRACM, Composikey, and ITZKP as a means of augmenting security measures and reducing potential hazards in cloudbased systems. The execution times comparison of the Composikey, IBPRE, and KPRE models were compared for different filesizes (1 KB to 2 GB) to evaluate the performance of the HRACM method. As roles increase, RBAC a execution time increases significantly. The HRACM Method takes 0.001 to 0.002 seconds to implement across all role counts. The results show that the HRACM Method is more efficient and time-effective than the RBAC Method. The response time measured in microseconds for the existing ZKP and Libra systems for different file sizes, ranging from 1KB to 1 GB. The results reveal that the verifier time for the ITZKP system aligns closely with the existing systems, demonstrating its ability to perform efficient verification processes. These findings collectively demonstrate the potential of the integrated security framework in enhancing cloud security.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"1057 ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138982714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a CRITIC-TOPSIS ''multi-criteria decision-making'' method under a neutrosophic environment. The neutrosophic set is a generalized version of the fuzzy and ''intuitionistic fuzzy set''. The purpose of this paper is the extension of the CRITIC-TOPSIS method using neutrosophic sets to create a more accurate and efficient decision support system for selecting a very light business jet (Bizjet). It provides the ranking to the selected number of Bizjets based on some pre-defined criteria under the neutrosophic CRITIC-TOPSIS method. The results of this study are obtained from the extended version of the previous study on decision-making for the selection of Bizjets. This study obtains results under the neutrosophic environment with a more realistic scenario.
{"title":"A CRITIC-TOPSIS MCDM Technique under the Neutrosophic Environment with Application on Aircraft Selection","authors":"Gurpreet Kaur, Aishwarya Dhara, Arunava Majumder, Balvinder Singh Sandhu, Avinandan Puhan, Manoj Singh Adhikari","doi":"10.37256/cm.4420232963","DOIUrl":"https://doi.org/10.37256/cm.4420232963","url":null,"abstract":"This paper develops a CRITIC-TOPSIS ''multi-criteria decision-making'' method under a neutrosophic environment. The neutrosophic set is a generalized version of the fuzzy and ''intuitionistic fuzzy set''. The purpose of this paper is the extension of the CRITIC-TOPSIS method using neutrosophic sets to create a more accurate and efficient decision support system for selecting a very light business jet (Bizjet). It provides the ranking to the selected number of Bizjets based on some pre-defined criteria under the neutrosophic CRITIC-TOPSIS method. The results of this study are obtained from the extended version of the previous study on decision-making for the selection of Bizjets. This study obtains results under the neutrosophic environment with a more realistic scenario.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 2","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138612986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The efficacy of the Markovian single server symmetric queue is examined in this paper together with the suggested encouraged stationary queue-size analysis. First, we propose the stochastic Markov renewal process with encouraged arrival see time averages and encouraged arrival-stationary-queue-size analysis. The server takes further vacations after two extra service phases or until the server discovers a new set of clients in the service. Finally, we discuss the utility of the Bernoulli two-vacation symmetric queue, and it is clearly shown that the degree of efficiency rises when the encouraged arrival is taken into account.
{"title":"Efficacy of the Single Server Markovian Two-Phase Symmetric Queue with Encouraged Stationary-Queue-Size Analysis","authors":"R. Jeyachandhiran, P. Rajendran","doi":"10.37256/cm.4420233505","DOIUrl":"https://doi.org/10.37256/cm.4420233505","url":null,"abstract":"The efficacy of the Markovian single server symmetric queue is examined in this paper together with the suggested encouraged stationary queue-size analysis. First, we propose the stochastic Markov renewal process with encouraged arrival see time averages and encouraged arrival-stationary-queue-size analysis. The server takes further vacations after two extra service phases or until the server discovers a new set of clients in the service. Finally, we discuss the utility of the Bernoulli two-vacation symmetric queue, and it is clearly shown that the degree of efficiency rises when the encouraged arrival is taken into account.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139223424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let η be a network graph with vertex and edge sets P(η) and E(η), respectively. This study aims to find the expected value (obtained during training and testing data) for Artificial Neural Networks (ANN) through indices. A three-layer artificial neural network is considered here, which we call ANN(m, n, o). Moreover, a comparison is given between the topological indices (TI) of ANN with topological indices (TI) of the Probabilistic Neural Network (PNN). By comparing the indices, we can assess the effect of network structure on ANN model accuracy. The comparison between the two approaches helps us understand the accuracy and performance of ANN and PNN models. We can also gain insights into the differences between ANN and PNN in terms of their ability to learn and generalize.
假设 η 是一个网络图，其顶点和边集分别为 P(η) 和 E(η)。本研究旨在通过指数找到人工神经网络（ANN）的预期值（在训练和测试数据期间获得）。这里考虑的是三层人工神经网络，我们称之为 ANN（m、n、o）。此外，我们还将 ANN 的拓扑指数 (TI) 与概率神经网络 (PNN) 的拓扑指数 (TI) 进行了比较。通过比较这些指数，我们可以评估网络结构对 ANN 模型准确性的影响。这两种方法之间的比较有助于我们了解 ANN 和 PNN 模型的准确性和性能。我们还可以深入了解 ANN 和 PNN 在学习和泛化能力方面的差异。
{"title":"Computing Topological Indices of 3-Layered Artificial Neural Network","authors":"Gayathiri V, Manimaran A","doi":"10.37256/cm.4420233502","DOIUrl":"https://doi.org/10.37256/cm.4420233502","url":null,"abstract":"Let η be a network graph with vertex and edge sets P(η) and E(η), respectively. This study aims to find the expected value (obtained during training and testing data) for Artificial Neural Networks (ANN) through indices. A three-layer artificial neural network is considered here, which we call ANN(m, n, o). Moreover, a comparison is given between the topological indices (TI) of ANN with topological indices (TI) of the Probabilistic Neural Network (PNN). By comparing the indices, we can assess the effect of network structure on ANN model accuracy. The comparison between the two approaches helps us understand the accuracy and performance of ANN and PNN models. We can also gain insights into the differences between ANN and PNN in terms of their ability to learn and generalize.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"73 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139241583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hemlata Sahu, Ramgopal Kashyap, Surbhi Bhatia, B. Dewangan, Nora A. Alkhaldi, Samson Anosh Babu, Senthilkumar Mohan
In this paper, artificial intelligence (AI) and the ideas of machine learning (ML) and deep learning (DL) are introduced gradually. Applying ML techniques like deep neural network (DNN) models has grown in popularity in recent years due to the complexity of healthcare data, which has been increasing. To extract hidden patterns and some other crucial information from the enormous amount of health data, which traditional analytics are unable to locate in a fair amount of time, ML approaches offer cost-effective and productive models for data analysis. We are encouraged to pursue this work because of the quick advancements made in DL approaches. The idea of DL is developing from its theoretical foundations to its applications. Modern ML models that are widely utilized in academia and industry, mostly in image classification and natural language processing, including DNN. Medical imaging technologies, medical healthcare data processing, medical disease diagnostics, and general healthcare all stand to greatly benefit from these developments. We have two goals: first, to conduct a survey on DL techniques for medical pictures, and second, to develop DL-based approaches for image classification. This paper is mainly targeted towards understanding the feasibility and different processes that could be adopted for medical image classification; for this, we perform a systematic literature review. A review of various existing techniques in terms of medical image classification indicates some shortcomings that have an impact on the performance of the whole model. This study aims to explore the existing DL approaches, challenges, brief comparisons, and applicability of different medical image processing are also studied and presented. The adoption of fewer datasets, poor use of temporal information, and reduced classification accuracy all contribute to the lower performance model, which is addressed. The study provides a clear explanation of contemporary developments, cutting-edge learning tools, and platforms for DL techniques.
本文将逐步介绍人工智能（AI）以及机器学习（ML）和深度学习（DL）的思想。近年来，由于医疗数据的复杂性不断增加，应用深度神经网络（DNN）模型等 ML 技术越来越受欢迎。要从海量医疗数据中提取传统分析方法无法在短时间内找到的隐藏模式和其他一些关键信息，ML 方法为数据分析提供了具有成本效益且富有成效的模型。由于 DL 方法的快速发展，我们深受鼓舞地开展了这项工作。DL 的理念正在从理论基础向应用发展。现代 ML 模型在学术界和工业界得到广泛应用，主要用于图像分类和自然语言处理，包括 DNN。医学成像技术、医疗保健数据处理、医疗疾病诊断和普通医疗保健都将从这些发展中受益匪浅。我们有两个目标：第一，对医学图像的 DL 技术进行调查；第二，开发基于 DL 的图像分类方法。本文的主要目标是了解医学图像分类的可行性和可采用的不同流程；为此，我们进行了系统的文献综述。对现有各种医学影像分类技术的回顾表明，这些技术存在一些缺点，会影响整个模型的性能。本研究旨在探讨现有的 DL 方法、挑战、简要比较以及不同医学图像处理的适用性。采用较少的数据集、对时间信息的利用不佳以及分类准确性的降低都是造成模型性能较低的原因，本研究对此进行了探讨。本研究清楚地解释了 DL 技术的当代发展、前沿学习工具和平台。
{"title":"Analysis of Deep Learning Methods for Healthcare Sector - Medical Imaging Disease Detection","authors":"Hemlata Sahu, Ramgopal Kashyap, Surbhi Bhatia, B. Dewangan, Nora A. Alkhaldi, Samson Anosh Babu, Senthilkumar Mohan","doi":"10.37256/cm.4420232496","DOIUrl":"https://doi.org/10.37256/cm.4420232496","url":null,"abstract":"In this paper, artificial intelligence (AI) and the ideas of machine learning (ML) and deep learning (DL) are introduced gradually. Applying ML techniques like deep neural network (DNN) models has grown in popularity in recent years due to the complexity of healthcare data, which has been increasing. To extract hidden patterns and some other crucial information from the enormous amount of health data, which traditional analytics are unable to locate in a fair amount of time, ML approaches offer cost-effective and productive models for data analysis. We are encouraged to pursue this work because of the quick advancements made in DL approaches. The idea of DL is developing from its theoretical foundations to its applications. Modern ML models that are widely utilized in academia and industry, mostly in image classification and natural language processing, including DNN. Medical imaging technologies, medical healthcare data processing, medical disease diagnostics, and general healthcare all stand to greatly benefit from these developments. We have two goals: first, to conduct a survey on DL techniques for medical pictures, and second, to develop DL-based approaches for image classification. This paper is mainly targeted towards understanding the feasibility and different processes that could be adopted for medical image classification; for this, we perform a systematic literature review. A review of various existing techniques in terms of medical image classification indicates some shortcomings that have an impact on the performance of the whole model. This study aims to explore the existing DL approaches, challenges, brief comparisons, and applicability of different medical image processing are also studied and presented. The adoption of fewer datasets, poor use of temporal information, and reduced classification accuracy all contribute to the lower performance model, which is addressed. The study provides a clear explanation of contemporary developments, cutting-edge learning tools, and platforms for DL techniques.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"50 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139263232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.
设 p ≥ 11 为奇数素数，q = 2(p - 1)。假设 n ≥ 1，n≠5。设 0≤s < p - 4，且 t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s + 4)p3 + pn。本文证明了乘积元素 δs+4h0bn-1∈ ExtAs+7,tq+s (Z/p,Z/p) 是经典亚当斯谱序列中的一个非小永久循环，其中 δs+4 表示第 4 个希腊字母元素。
{"title":"On Nontriviality of a Product in the Classical Adams Spectral Sequence","authors":"Linan Zhong, Hao Zhao","doi":"10.37256/cm.4420232994","DOIUrl":"https://doi.org/10.37256/cm.4420232994","url":null,"abstract":"Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"47 4","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139265141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present paper aims at providing an insight to embedded Runge-Kutta sixth order (RKSD) ordinary differential equation method for solving the initial value problem of order six of type vvi(u) = f(u, v, v', v'',v''',viv). The concept of order conditions for the three and four stages up to the eighth and ninth orders, respectively, is designed and evaluated; furthermore, the zero-stability of the proposed method is proved. Comparisons are made between these orders with the help of a mathematical example, and global and local truncated error norms are evaluated.
{"title":"Error Analysis Using Three and Four Stage Eighth Order Embedded Runge-Kutta Method for Sixth Order Ordinary Differential Equation vvi(u)=f(u,v,v',v'',v''',viv)","authors":"Manpreet Kaur, Sangeet Kumar, J. Bhatti","doi":"10.37256/cm.4420232610","DOIUrl":"https://doi.org/10.37256/cm.4420232610","url":null,"abstract":"The present paper aims at providing an insight to embedded Runge-Kutta sixth order (RKSD) ordinary differential equation method for solving the initial value problem of order six of type vvi(u) = f(u, v, v', v'',v''',viv). The concept of order conditions for the three and four stages up to the eighth and ninth orders, respectively, is designed and evaluated; furthermore, the zero-stability of the proposed method is proved. Comparisons are made between these orders with the help of a mathematical example, and global and local truncated error norms are evaluated.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"9 3","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139275323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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