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.
{"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}
{"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}
Ardjouma Ganon, Manin Mathurin Taha, N’guessan Koffi, A. Toure
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.
本文研究了非线性扩散方程(u)t = uxx, 0 < x < 1, t > 0，在Neumann边界条件下ux(0, t) = 0, ux(1, t) = uα(1, t)， t > 0的数值逼近。首先，利用有限差分法得到了半离散格式，并证明了其解对连续格式的收敛性。然后，我们建立了数值爆破和当网格尺寸趋近于零时数值爆破时间与理论爆破时间的收敛性。最后，我们用一些数值实验来说明我们的分析。
{"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}
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.
它由[A]L. Dontchev, R. T. Rockafellar, Springer, New York， (2014)， Theorem 5I。3]点x到集值收缩映射Φ的不动点集的距离以一个常数乘以x到Φ(x)的距离为界。在本文中，我们将这一结果和Lim引理推广到一个更大的集值映射类，而不是集值收缩映射类。由此，我们得到了一些已知的不动点定理。
{"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}
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.
{"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}
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.
{"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}
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.
本文提出了一种基于sinc节点sinc近似的求解非局部边界条件抛物型偏微分方程的简单方法。Sinc近似的典型误差形式为O (e - k/h)，其中k > 0是一个常数，h是一个步长。算例表明了该方法的有效性和精度。该方法灵活、易于编程、效率高。
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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