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Numerical solutions of nonlinear fractional differential equations by variational iteration method 非线性分数阶微分方程的变分迭代数值解
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-07-03 DOI: 10.22436/jnsa.014.02.01
A. Nagdy, KH. M. Hashem
{"title":"Numerical solutions of nonlinear fractional differential equations by variational iteration method","authors":"A. Nagdy, KH. M. Hashem","doi":"10.22436/jnsa.014.02.01","DOIUrl":"https://doi.org/10.22436/jnsa.014.02.01","url":null,"abstract":"In this paper, numerical techniques are used for solving boundary value problems of nonlinear fractional differential equations. Variational iteration method is applied to approximate solutions for this equation with boundary conditions. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed method, and we compare between the numerical solutions and the exact solution of these examples.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"30 1","pages":"54-62"},"PeriodicalIF":0.0,"publicationDate":"2020-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91208350","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}
引用次数: 1
Strong convergence theorems for mixed equilibrium problems and Bregman relatively nonexpansive mappings in reflexive Banach spaces 自反Banach空间中混合平衡问题和Bregman相对非扩张映射的强收敛定理
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-07-03 DOI: 10.22436/jnsa.014.02.02
Kittisak Jantakarn, A. Kaewcharoen
{"title":"Strong convergence theorems for mixed equilibrium problems and Bregman relatively nonexpansive mappings in reflexive Banach spaces","authors":"Kittisak Jantakarn, A. Kaewcharoen","doi":"10.22436/jnsa.014.02.02","DOIUrl":"https://doi.org/10.22436/jnsa.014.02.02","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"47 1","pages":"63-79"},"PeriodicalIF":0.0,"publicationDate":"2020-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77243211","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}
引用次数: 1
Numerical blow-up for nonlinear diffusion equation with neumann boundary conditions 具有neumann边界条件的非线性扩散方程的数值爆破
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-07-03 DOI: 10.22436/jnsa.014.02.03
Ardjouma Ganon, Manin Mathurin Taha, N’guessan Koffi, A. Toure
{"title":"Numerical blow-up for nonlinear diffusion equation with neumann boundary conditions","authors":"Ardjouma Ganon, Manin Mathurin Taha, N’guessan Koffi, A. Toure","doi":"10.22436/jnsa.014.02.03","DOIUrl":"https://doi.org/10.22436/jnsa.014.02.03","url":null,"abstract":"This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation (u)t = uxx, 0 < x < 1, t > 0, under Neumann boundary conditions ux(0, t) = 0, ux(1, t) = uα(1, t), t > 0. First, we obtain a semidiscrete scheme by the finite differences method and prove the convergence of its solution to the continuous one. Then, we establish the numerical blow-up and the convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero. Finally, we illustrate our analysis with some numerical experiments.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"35 1","pages":"80-88"},"PeriodicalIF":0.0,"publicationDate":"2020-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89478254","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}
引用次数: 0
A generalization of Lim's lemma 林氏引理的推广
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-06-13 DOI: 10.22436/jnsa.014.01.06
M. Mansour, M. Bahraoui, A. E. Bekkali
{"title":"A generalization of Lim's lemma","authors":"M. Mansour, M. Bahraoui, A. E. Bekkali","doi":"10.22436/jnsa.014.01.06","DOIUrl":"https://doi.org/10.22436/jnsa.014.01.06","url":null,"abstract":"It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point x to the set of fixed points of a set-valued contraction mapping Φ is bounded by a constant times the distance from x to Φ(x). In this paper, we generalize both this result and Lim’s lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":"48-53"},"PeriodicalIF":0.0,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83109286","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}
引用次数: 0
Fixed point results for (β,α)-implicit contractions in two generalized b-metric spaces 两个广义b-度量空间中(β，α)-隐缩的不动点结果
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-06-13 DOI: 10.22436/jnsa.014.01.05
G. M. Abd-Elhamed
{"title":"Fixed point results for (β,α)-implicit contractions in two generalized b-metric spaces","authors":"G. M. Abd-Elhamed","doi":"10.22436/jnsa.014.01.05","DOIUrl":"https://doi.org/10.22436/jnsa.014.01.05","url":null,"abstract":"The aim of this paper is to introduce (β,α)-implicit contractive of two mappings on two generalized b-metric spaces and derive some new fixed point theorems for (β,α)-implicit contractive in two complete and compact generalized b-Metric spaces.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"106 1","pages":"39-47"},"PeriodicalIF":0.0,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75660953","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}
引用次数: 10
Nonlinear dynamics and synchronization of computational cognitive model in educational science 教育科学计算认知模型的非线性动力学与同步
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-06-13 DOI: 10.22436/jnsa.014.01.03
E. T. Akpan, E. E. Joshua, Ignatius E. Uduk
{"title":"Nonlinear dynamics and synchronization of computational cognitive model in educational science","authors":"E. T. Akpan, E. E. Joshua, Ignatius E. Uduk","doi":"10.22436/jnsa.014.01.03","DOIUrl":"https://doi.org/10.22436/jnsa.014.01.03","url":null,"abstract":"A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostkian constructs to explain, and predict cognitive processes during collaborative learning. Learning is re-conceptualized as continuous perturbations of cognitive state which unfolds stable cognitive trajectories near Piagetian equilibrium. The model explicates topologically equivalent cognitive patterns, attributed to multi-modal representation of sensory information presented to the learners. Synchronization of the cognitive model is obtained via active control functions which predicts convergence of cognitive states. The synchronized cognitive model is stabilized using Lyapunov matrix equation. These qualitative behaviors emerged due to learner-to-learner and instructor-to-learner scaffolding driven by cognitive executive functions. The dynamical behaviors of the cognitive model are simulated using control parameters with estimated datasets showing viable cognitive trajectories.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"s1-14 1","pages":"15-28"},"PeriodicalIF":0.0,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85969610","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}
引用次数: 1
On using sinc collocation approach for solving a parabolic PDE with nonlocal boundary conditions 用sinc配点法求解具有非局部边界条件的抛物型偏微分方程
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-06-13 DOI: 10.22436/jnsa.014.01.04
M. El-Gamel, M. El-Hady
{"title":"On using sinc collocation approach for solving a parabolic PDE with nonlocal boundary conditions","authors":"M. El-Gamel, M. El-Hady","doi":"10.22436/jnsa.014.01.04","DOIUrl":"https://doi.org/10.22436/jnsa.014.01.04","url":null,"abstract":"This work suggests a simple method based on a sinc approximation at sinc nodes for solving parabolic partial differential equations with nonlocal boundary conditions. Sinc approximation are typified by errors of the form O ( e−k/h ) , where k > 0 is a constant and h is a step size. Some numerical examples are utilized to reveal the efficaciousness and precision of this method. The suggested method is flexible, easy to programme and efficient.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"16 1","pages":"29-38"},"PeriodicalIF":0.0,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74018172","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}
引用次数: 0
Adaptive cluster sampling randomized response model with electronically application 电子应用的自适应整群抽样随机响应模型
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-04-28 DOI: 10.22436/jnsa.014.01.02
Mahmoud M. Mansour, E. A. Elrazik
{"title":"Adaptive cluster sampling randomized response model with electronically application","authors":"Mahmoud M. Mansour, E. A. Elrazik","doi":"10.22436/jnsa.014.01.02","DOIUrl":"https://doi.org/10.22436/jnsa.014.01.02","url":null,"abstract":"It is difficult to estimate sensitive matters (e.g., addiction, drunken driving, and abortion) in population distributed over a large geographical area by conventional designs of sampling because of the social, political and security conditions that usually lead to their concentration in certain areas. An adaptive sampling scheme extending the initial sample by appropriate ‘network’ formations dependent on well-defined ‘neighborhoods’ brings about dramatic improvements exploiting the clustering tendencies of people by different places. On another hand to reduce non-response and response bias was needed to make people comfortable and to encourage truthful answers. So also we introduce a new technique to apply a randomized response by tablets, computers, mobile phones and etc. The relative efficiency and protection of the respondents of the proposed randomization device have been investigated. We illustrate our methods using real data from a survey study on the spread of the addiction phenomenon among high school students.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"30 1","pages":"8-14"},"PeriodicalIF":0.0,"publicationDate":"2020-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84954064","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}
引用次数: 0
Statistical properties of type II Topp Leone inverse exponential distribution II型Topp Leone逆指数分布的统计性质
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-04-28 DOI: 10.22436/jnsa.014.01.01
Sanaa Al-Marzouki
{"title":"Statistical properties of type II Topp Leone inverse exponential distribution","authors":"Sanaa Al-Marzouki","doi":"10.22436/jnsa.014.01.01","DOIUrl":"https://doi.org/10.22436/jnsa.014.01.01","url":null,"abstract":"In this paper a new lifetime parameters model named the type II topp leone inverse exponential (TIITLIE) model is proposed. Some fundamental properties of the TIITLIE model are calculated. The maximum likelihood (ML) method of estimation are assessed to the parameters of TIITLIE distribution. The superiority of the TIITLIE model is showed by using 63 aircraft windshields real data set.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"77 1","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2020-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90847338","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}
引用次数: 2
On the symmetric positive solutions of nonlinear fourth order ordinary differential equations with four-point boundary value conditions: a fixed point theory approach 具有四点边值条件的非线性四阶常微分方程的对称正解:不动点理论方法
The Journal of Nonlinear Sciences and Applications Pub Date : 2020-04-25 DOI: 10.22436/jnsa.013.06.06
M. Asaduzzaman, Md. Zulfikar Ali
{"title":"On the symmetric positive solutions of nonlinear fourth order ordinary differential equations with four-point boundary value conditions: a fixed point theory approach","authors":"M. Asaduzzaman, Md. Zulfikar Ali","doi":"10.22436/jnsa.013.06.06","DOIUrl":"https://doi.org/10.22436/jnsa.013.06.06","url":null,"abstract":"The purpose of this paper is to investigate the existence of symmetric positive solutions of the following nonlinear fourth order system of ordinary differential equations{ −u(4)(t) = f(t, v), −v(4)(t) = g(t, u), t ∈ [0, 1], with the four-point boundary value conditions { u(t) = u(1 − t), u′′′(0) − u′′′(1) = u(t1) + u(t2), v(t) = v(1 − t), v′′′(0) − v′′′(1) = v(t1) + v(t2), 0 < t1 < t2 < 1. By applying Krasnoselskii’s fixed point theorem and under suitable conditions, we establish the existence of at least one or at least two symmetric positive solutions of the above mentioned fourth order four-point boundary value problem in cone. Some particular examples are provided to support the analytic proof.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"77 1","pages":"364-377"},"PeriodicalIF":0.0,"publicationDate":"2020-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86887812","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}
引用次数: 2
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