Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [14] introduced the concept of permanence as a stability notion for systems that models the self-organization of biological macromolecules. After, in 1987 W. Jansen [8], and J. Hofbauer and K. Sigmund [5] give sufficient conditions for permanence in the usual replicators. In this paper we extend these results for polymatrix replicators.
一般来说，如果在微小的扰动下没有一个物种走向灭绝，那么一个生物系统就被称为是永久的。1979年，P. Schuster, K. Sigmund和R. Wolff[14]引入了永久性的概念，作为模拟生物大分子自组织的系统的稳定性概念。之后，在1987年W。Jansen [8]， J. Hofbauer和K. Sigmund[8]给出了通常复制因子存在的充分条件。本文将这些结果推广到多矩阵复制子。
{"title":"Permanence in polymatrix replicators","authors":"Telmo Peixe","doi":"10.3934/jdg.2020032","DOIUrl":"https://doi.org/10.3934/jdg.2020032","url":null,"abstract":"Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [14] introduced the concept of permanence as a stability notion for systems that models the self-organization of biological macromolecules. After, in 1987 W. Jansen [8], and J. Hofbauer and K. Sigmund [5] give sufficient conditions for permanence in the usual replicators. In this paper we extend these results for polymatrix replicators.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70033793","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 article, we extend to private ownership production economies, the results presented by Bergstrom, Shimomura, and Yamato (2009) on the multiplicity of equilibria for the special kind of pure-exchanges economies called Shapley-Shubik economies. Furthermore, a dynamic system that represents the changes in the distribution of the firms on the production branches is introduced. For the first purpose, we introduce a particular, but large enough, production sector to the Shapley-Shubik economies, for which a simple technique to build private-ownership economies with a multiplicity of equilibria is developed. In this context, we analyze the repercussions on the behavior of the economy when the number of possible equilibria changes due to rational decisions on the production side. For the second purpose, we assume that the rational decisions on the production side provoke a change in the distribution of the firms over the set of branches of production.
{"title":"A dynamic for production economies with multiple equilibria","authors":"E. Accinelli, H. Muñiz","doi":"10.3934/jdg.2021002","DOIUrl":"https://doi.org/10.3934/jdg.2021002","url":null,"abstract":"In this article, we extend to private ownership production economies, the results presented by Bergstrom, Shimomura, and Yamato (2009) on the multiplicity of equilibria for the special kind of pure-exchanges economies called Shapley-Shubik economies. Furthermore, a dynamic system that represents the changes in the distribution of the firms on the production branches is introduced. For the first purpose, we introduce a particular, but large enough, production sector to the Shapley-Shubik economies, for which a simple technique to build private-ownership economies with a multiplicity of equilibria is developed. In this context, we analyze the repercussions on the behavior of the economy when the number of possible equilibria changes due to rational decisions on the production side. For the second purpose, we assume that the rational decisions on the production side provoke a change in the distribution of the firms over the set of branches of production.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70033870","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}
Based on a work by M. Dur and J.-B. Hiriart-Urruty[3], we consider the problem of whether a symmetric matrix is copositive formulated as a difference of convex functions problem. The convex nondifferentiable function in this d.c. decomposition being proximable, we then apply a proximal-gradient method to approximate the related stationary points. Whereas, in [3], the DCA algorithm was used.
{"title":"Copositivity meets D. C. optimization","authors":"A. Moudafi, P. Maingé","doi":"10.3934/jdg.2021022","DOIUrl":"https://doi.org/10.3934/jdg.2021022","url":null,"abstract":"<p style='text-indent:20px;'>Based on a work by M. Dur and J.-B. Hiriart-Urruty[<xref ref-type=\"bibr\" rid=\"b3\">3</xref>], we consider the problem of whether a symmetric matrix is copositive formulated as a difference of convex functions problem. The convex nondifferentiable function in this d.c. decomposition being proximable, we then apply a proximal-gradient method to approximate the related stationary points. Whereas, in [<xref ref-type=\"bibr\" rid=\"b3\">3</xref>], the DCA algorithm was used.</p>","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70034421","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}
We study a two player zero sum game where the initial position begin{document}$ z_0 $end{document} is not communicated to any player. The initial position is a function of a couple begin{document}$ (x_0,y_0) $end{document} where begin{document}$ x_0 $end{document} is communicated to player Ⅰ while begin{document}$ y_0 $end{document} is communicated to player Ⅱ. The couple begin{document}$ (x_0,y_0) $end{document} is chosen according to a probability measure begin{document}$ dm(x,y) = h(x,y) dmu(x) dnu(y) $end{document} . We show that the game has a value and, under additional regularity assumptions, that the value is a solution of Hamilton Jacobi Isaacs equation in a dual sense.
We study a two player zero sum game where the initial position begin{document}$ z_0 $end{document} is not communicated to any player. The initial position is a function of a couple begin{document}$ (x_0,y_0) $end{document} where begin{document}$ x_0 $end{document} is communicated to player Ⅰ while begin{document}$ y_0 $end{document} is communicated to player Ⅱ. The couple begin{document}$ (x_0,y_0) $end{document} is chosen according to a probability measure begin{document}$ dm(x,y) = h(x,y) dmu(x) dnu(y) $end{document} . We show that the game has a value and, under additional regularity assumptions, that the value is a solution of Hamilton Jacobi Isaacs equation in a dual sense.
{"title":"A zero sum differential game with correlated informations on the initial position. A case with a continuum of initial positions","authors":"C. Jimenez","doi":"10.3934/JDG.2021009","DOIUrl":"https://doi.org/10.3934/JDG.2021009","url":null,"abstract":"We study a two player zero sum game where the initial position begin{document}$ z_0 $end{document} is not communicated to any player. The initial position is a function of a couple begin{document}$ (x_0,y_0) $end{document} where begin{document}$ x_0 $end{document} is communicated to player Ⅰ while begin{document}$ y_0 $end{document} is communicated to player Ⅱ. The couple begin{document}$ (x_0,y_0) $end{document} is chosen according to a probability measure begin{document}$ dm(x,y) = h(x,y) dmu(x) dnu(y) $end{document} . We show that the game has a value and, under additional regularity assumptions, that the value is a solution of Hamilton Jacobi Isaacs equation in a dual sense.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70034509","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 2016–2018 triennium was a period marked by a fierce dispute between the European Commission and Autoridade Nacional de Comunicações, Portugal, on the need to regulate wholesale access prices. While the European Commission defended the imposition of Fiber-To-The-x regulation in non-competitive areas, the Portuguese sectoral regulator argued in favor of the persistence of Fiber-To-The-x deregulation. Following a Game Theory approach, the present study demonstrates that the transition from Fiber-To-The-x deregulation to Fiber-To-The-x regulation should only occur when a given territorial unit becomes a competitive area since the subgame perfect Nash equilibrium captures a regulatory framework optimally characterized by the imposition of active access price deregulation (regulation) in non-competitive (competitive) areas, that is, local administrative units characterized by a weak (strong) degree of vertical spillover, respectively. Meanwhile, ducts access regulation must be permanently imposed throughout the national territory, despite it can be relaxed in competitive areas if the regulator imposes intra-flexibility to establish a monopolistic bottleneck to ensure social welfare maximization. Previous conclusions require to introduce both facility-based and service-based competition at the entry stage as well as active and passive obligations at the regulation stage in a multi-stage game with complete information. The present analysis legitimizes the emergence of a new optimization theory in the telecommunications literature, whose modus operandi is contrary to (coincident with) the ladder of investment theory in non-competitive (competitive) areas, respectively. Differently from the view sustained by the ladder of investment theory, which defends that a short-term regulatory touch combined with long-term market deregulation is a socially optimal strategy, the new theory confirms that a regulatory intervention is socially desirable only in the long run. The conceptual refinement is meticulously explained and labeled as the theory of creative creation because, differently from the Schumpeterian gale of creative destruction, whose processes of industrial mutation are permanently market-driven by assumption, a period of regulatory holidays followed by successive regulatory interventions dependent on the degree of vertical spillover observed in the telecommunications industry can effectively promote investment realization that continuously revolutionizes the market structure from within, incessantly destroying the old technology. The theory of creative creation reflects the regulatory framework currently in force in the Portuguese Telecommunications Industry.
2016-2018三年期间，欧盟委员会(European Commission)与葡萄牙国家高速公路(Autoridade Nacional de Comunicações)就监管批发接入价格的必要性发生了激烈争执。虽然欧盟委员会为在非竞争领域实施光纤到无线监管辩护，但葡萄牙部门监管机构辩称，支持继续放松光纤到无线监管。根据博弈论的方法，本研究表明，从光纤到光纤的监管过渡到光纤到光纤的监管应该只发生在给定的领土单位成为竞争区域时，因为子博弈完美纳什均衡捕获了一个监管框架，其最佳特征是在非竞争(竞争)区域实施主动接入价格放松管制(监管)，即:地方行政单位垂直溢出分别表现为弱(强)度。与此同时，管道准入监管必须在全国范围内永久实施，尽管如果监管机构施加内部灵活性以建立垄断瓶颈以确保社会福利最大化，则可以在竞争领域放松监管。以往的结论要求在完全信息的多阶段博弈中，在准入阶段引入以设施为基础的竞争和以服务为基础的竞争，在监管阶段引入主动义务和被动义务。目前的分析证明了电信文献中出现的一种新的优化理论是合理的，这种理论的运作方式分别与非竞争性(竞争性)领域的投资阶梯理论相反(一致)。与投资阶梯理论所支持的观点不同，该理论认为，短期监管与长期市场放松管制相结合是一种社会最优策略，而新理论证实，监管干预只有在长期内才是社会理想的。这一概念的细化被细致地解释并贴上了创造性创造理论的标签，因为与熊彼特的创造性破坏理论不同，熊彼特的创造性破坏理论的工业突变过程永远是由假设驱动的，根据电信行业的垂直溢出程度，在一段时间的监管假期之后进行连续的监管干预，可以有效地促进投资实现，从而不断地从内部彻底改变市场结构，不断地破坏旧技术。创造性创造理论反映了葡萄牙电信业目前有效的监管框架。
{"title":"Explaining the definition of wholesale access prices in the Portuguese telecommunications industry","authors":"V. Ribeiro, F. L. Pereira, Rui Gonçalves","doi":"10.3934/jdg.2021024","DOIUrl":"https://doi.org/10.3934/jdg.2021024","url":null,"abstract":"The 2016–2018 triennium was a period marked by a fierce dispute between the European Commission and Autoridade Nacional de Comunicações, Portugal, on the need to regulate wholesale access prices. While the European Commission defended the imposition of Fiber-To-The-x regulation in non-competitive areas, the Portuguese sectoral regulator argued in favor of the persistence of Fiber-To-The-x deregulation. Following a Game Theory approach, the present study demonstrates that the transition from Fiber-To-The-x deregulation to Fiber-To-The-x regulation should only occur when a given territorial unit becomes a competitive area since the subgame perfect Nash equilibrium captures a regulatory framework optimally characterized by the imposition of active access price deregulation (regulation) in non-competitive (competitive) areas, that is, local administrative units characterized by a weak (strong) degree of vertical spillover, respectively. Meanwhile, ducts access regulation must be permanently imposed throughout the national territory, despite it can be relaxed in competitive areas if the regulator imposes intra-flexibility to establish a monopolistic bottleneck to ensure social welfare maximization. Previous conclusions require to introduce both facility-based and service-based competition at the entry stage as well as active and passive obligations at the regulation stage in a multi-stage game with complete information. The present analysis legitimizes the emergence of a new optimization theory in the telecommunications literature, whose modus operandi is contrary to (coincident with) the ladder of investment theory in non-competitive (competitive) areas, respectively. Differently from the view sustained by the ladder of investment theory, which defends that a short-term regulatory touch combined with long-term market deregulation is a socially optimal strategy, the new theory confirms that a regulatory intervention is socially desirable only in the long run. The conceptual refinement is meticulously explained and labeled as the theory of creative creation because, differently from the Schumpeterian gale of creative destruction, whose processes of industrial mutation are permanently market-driven by assumption, a period of regulatory holidays followed by successive regulatory interventions dependent on the degree of vertical spillover observed in the telecommunications industry can effectively promote investment realization that continuously revolutionizes the market structure from within, incessantly destroying the old technology. The theory of creative creation reflects the regulatory framework currently in force in the Portuguese Telecommunications Industry.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70034537","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}
Adriano Festa, D. Gomes, Francisco J. Silva, D. Tonon
{"title":"Preface: Mean field games: New trends and applications","authors":"Adriano Festa, D. Gomes, Francisco J. Silva, D. Tonon","doi":"10.3934/jdg.2021025","DOIUrl":"https://doi.org/10.3934/jdg.2021025","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70034602","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}
Given two stable matchings in a many-to-one matching market with begin{document}$ q $end{document} -responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least upper bound and greatest lower bound between them.
Given two stable matchings in a many-to-one matching market with begin{document}$ q $end{document} -responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least upper bound and greatest lower bound between them.
{"title":"A note on the lattice structure for matching markets via linear programming","authors":"P. Neme, San Luis Argentina Av. Italia, J. Oviedo","doi":"10.3934/jdg.2021001","DOIUrl":"https://doi.org/10.3934/jdg.2021001","url":null,"abstract":"Given two stable matchings in a many-to-one matching market with begin{document}$ q $end{document} -responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least upper bound and greatest lower bound between them.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70033812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Leventides, C. Poulios, Georgios Alkis Tsiatsios, M. Livada, Stavros Tsipras, Konstantinos Lefcaditis, P. Sargenti, A. Sargenti
We utilize systems theory in the study of the implementation of non pharmaceutical strategies for the mitigation of the COVID-19 pandemic. We present two models. The first one is a model of predictive control with receding horizon and discontinuous actions of unknown costs for the implementation of adaptive triggering policies during the disease. This model is based on a periodic assessment of the peak of the pandemic (and, thus, of the health care demand) utilizing the latest data about the transmission and recovery rate of the disease. Consequently, the model seems to be suitable for discontinuous, non-mechanical (i.e. human) actions with unknown effectiveness, like those applied in the case of COVID-19. Secondly, we consider a feedback control problem in order to contain the pandemic at the capacity of the NHS (National Health System). As input parameter we consider the value begin{document}$ p $end{document} that reflects the intensity-effectiveness of the measures applied and as output the predicted maximum of infected people to be treated by NHS. The feedback control regulates begin{document}$ p $end{document} so that the number of infected people is manageable. Based on this approach, we address the following questions: (a) the limits of improvement of this approach; (b) the effectiveness of this approach; (c) the time horizon and timing of the application.
We utilize systems theory in the study of the implementation of non pharmaceutical strategies for the mitigation of the COVID-19 pandemic. We present two models. The first one is a model of predictive control with receding horizon and discontinuous actions of unknown costs for the implementation of adaptive triggering policies during the disease. This model is based on a periodic assessment of the peak of the pandemic (and, thus, of the health care demand) utilizing the latest data about the transmission and recovery rate of the disease. Consequently, the model seems to be suitable for discontinuous, non-mechanical (i.e. human) actions with unknown effectiveness, like those applied in the case of COVID-19. Secondly, we consider a feedback control problem in order to contain the pandemic at the capacity of the NHS (National Health System). As input parameter we consider the value begin{document}$ p $end{document} that reflects the intensity-effectiveness of the measures applied and as output the predicted maximum of infected people to be treated by NHS. The feedback control regulates begin{document}$ p $end{document} so that the number of infected people is manageable. Based on this approach, we address the following questions: (a) the limits of improvement of this approach; (b) the effectiveness of this approach; (c) the time horizon and timing of the application.
{"title":"Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic","authors":"J. Leventides, C. Poulios, Georgios Alkis Tsiatsios, M. Livada, Stavros Tsipras, Konstantinos Lefcaditis, P. Sargenti, A. Sargenti","doi":"10.3934/JDG.2021004","DOIUrl":"https://doi.org/10.3934/JDG.2021004","url":null,"abstract":"We utilize systems theory in the study of the implementation of non pharmaceutical strategies for the mitigation of the COVID-19 pandemic. We present two models. The first one is a model of predictive control with receding horizon and discontinuous actions of unknown costs for the implementation of adaptive triggering policies during the disease. This model is based on a periodic assessment of the peak of the pandemic (and, thus, of the health care demand) utilizing the latest data about the transmission and recovery rate of the disease. Consequently, the model seems to be suitable for discontinuous, non-mechanical (i.e. human) actions with unknown effectiveness, like those applied in the case of COVID-19. Secondly, we consider a feedback control problem in order to contain the pandemic at the capacity of the NHS (National Health System). As input parameter we consider the value begin{document}$ p $end{document} that reflects the intensity-effectiveness of the measures applied and as output the predicted maximum of infected people to be treated by NHS. The feedback control regulates begin{document}$ p $end{document} so that the number of infected people is manageable. Based on this approach, we address the following questions: (a) the limits of improvement of this approach; (b) the effectiveness of this approach; (c) the time horizon and timing of the application.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70033914","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, we focus on the equal surplus sharing interval solutions for cooperative games, where the set of players are finite and the coalition values are interval numbers. We consider the properties of a class of equal surplus sharing interval solutions consisting of all convex combinations of them. Moreover, an application based on transportation interval situations is given. Finally, we propose three solution concepts, namely the interval Shapley value, ICIS-value and IENSC-value, for this application and these solution concepts are compared.
{"title":"On the equal surplus sharing interval solutions and an application","authors":"O. Palanci, M. Eki̇ci̇, S. Z. A. Gök","doi":"10.3934/jdg.2020023","DOIUrl":"https://doi.org/10.3934/jdg.2020023","url":null,"abstract":"In this paper, we focus on the equal surplus sharing interval solutions for cooperative games, where the set of players are finite and the coalition values are interval numbers. We consider the properties of a class of equal surplus sharing interval solutions consisting of all convex combinations of them. Moreover, an application based on transportation interval situations is given. Finally, we propose three solution concepts, namely the interval Shapley value, ICIS-value and IENSC-value, for this application and these solution concepts are compared.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70034155","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}
We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.
{"title":"New solutions of hyperbolic telegraph equation","authors":"Mohammad Partohaghighi, M. Akinlar, G. Weber","doi":"10.3934/jdg.2020029","DOIUrl":"https://doi.org/10.3934/jdg.2020029","url":null,"abstract":"We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70034226","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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