Pub Date : 2025-01-03DOI: 10.1016/j.amc.2024.129265
Marcelo V. Flamarion, Efim Pelinovsky
In this article, we consider the cubic vortical Whitham equation with both positive and negative nonlinearity to investigate overtaking solitary wave collisions. We compute solitary waves numerically, including “thick” solitary waves. Our results show that in both cases, the geometric Lax categorization holds, however, it is independent of the magnitude of the amplitude of the solitary waves. Besides, for negative cubic nonlinearity, we compute thick solitary waves and investigate their paired interactions. Moreover, we show that Gardner solitons and CV-Whitham solitary waves have nearly the same shape and speed when the sign of cubic nonlinearity term is negative.
{"title":"Features of the interaction of paired solitary waves with the Cubic Vortical Whitham equation","authors":"Marcelo V. Flamarion, Efim Pelinovsky","doi":"10.1016/j.amc.2024.129265","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129265","url":null,"abstract":"In this article, we consider the cubic vortical Whitham equation with both positive and negative nonlinearity to investigate overtaking solitary wave collisions. We compute solitary waves numerically, including “thick” solitary waves. Our results show that in both cases, the geometric Lax categorization holds, however, it is independent of the magnitude of the amplitude of the solitary waves. Besides, for negative cubic nonlinearity, we compute thick solitary waves and investigate their paired interactions. Moreover, we show that Gardner solitons and CV-Whitham solitary waves have nearly the same shape and speed when the sign of cubic nonlinearity term is negative.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"34 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.amc.2024.129257
Sangeetha Rajendran, Palanivel Kaliyaperumal
This study addresses the synchronization problem of grid-connected permanent magnet synchronous motors (PMSMs)-based wind energy conversion systems (WECSs). This study significantly enhances the existing WECSs into the four-dimensional hyperchaotic grid-connected WECSs by integrating the impact of a DC-link capacitor. Moreover, this study treats the aerodynamics of WECSs as stochastic differential equations (SDEs), taking into account the random nature of wind-speed characteristics. Further, the nonlinearities in WECSs are approximated to linear form through Takagi-Sugeno (T–S) fuzzy with the help of IF-THEN membership rules. Each IF-THEN membership rule represents a local linear model valid around specific operating bounds. Moreover, this study considers an adaptive continuous feedback controller scheme to ensure the fixed-time synchronization between WECSs with and without control input. This study utilizes mathematical techniques such as Lyapunov stability theory and Ito's calculus theory to derive the analytical settling-time (ST) expression. This expression aids in identifying the time frame that ensures the convergence of the error model. As an application, this study designs an encryption and decryption algorithm by utilizing the hyperchaotic WECSs as a cryptosystem that may outperform the existing algorithms proposed for secure communications.
{"title":"Prescribed-time synchronization of hyperchaotic fuzzy stochastic PMSM model with an application to secure communications","authors":"Sangeetha Rajendran, Palanivel Kaliyaperumal","doi":"10.1016/j.amc.2024.129257","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129257","url":null,"abstract":"This study addresses the synchronization problem of grid-connected permanent magnet synchronous motors (PMSMs)-based wind energy conversion systems (WECSs). This study significantly enhances the existing WECSs into the four-dimensional hyperchaotic grid-connected WECSs by integrating the impact of a DC-link capacitor. Moreover, this study treats the aerodynamics of WECSs as stochastic differential equations (SDEs), taking into account the random nature of wind-speed characteristics. Further, the nonlinearities in WECSs are approximated to linear form through Takagi-Sugeno (T–S) fuzzy with the help of IF-THEN membership rules. Each IF-THEN membership rule represents a local linear model valid around specific operating bounds. Moreover, this study considers an adaptive continuous feedback controller scheme to ensure the fixed-time synchronization between WECSs with and without control input. This study utilizes mathematical techniques such as Lyapunov stability theory and Ito's calculus theory to derive the analytical settling-time (ST) expression. This expression aids in identifying the time frame that ensures the convergence of the error model. As an application, this study designs an encryption and decryption algorithm by utilizing the hyperchaotic WECSs as a cryptosystem that may outperform the existing algorithms proposed for secure communications.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"76 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.amc.2024.129252
Hossein Hosseinzadeh, Zeinab Sedaghatjoo
Conventionally, piecewise polynomials have been used in the boundary element method (BEM) to approximate unknown boundary values. However, since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for high dimensional domains, this paper proposes approximating the unknown values using RBFs. This new formulation is called the radial BEM. To calculate the singular boundary integrals in the radial BEM, the authors propose a new distribution of boundary source points that removes the singularity from the integrals. This allows the boundary integrals to be precisely calculated using the standard Gaussian quadrature rule with 16 quadrature nodes. Several numerical examples are presented to evaluate the efficiency of the radial BEM compared to standard BEM and RBF collocation method for solving partial differential equations (PDEs). The analytical and numerical studies demonstrate that the radial BEM is a superior version of BEM that will significantly enhance the application of BEM and RBFs in solving PDEs.
{"title":"Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently","authors":"Hossein Hosseinzadeh, Zeinab Sedaghatjoo","doi":"10.1016/j.amc.2024.129252","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129252","url":null,"abstract":"Conventionally, piecewise polynomials have been used in the boundary element method (BEM) to approximate unknown boundary values. However, since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for high dimensional domains, this paper proposes approximating the unknown values using RBFs. This new formulation is called the radial BEM. To calculate the singular boundary integrals in the radial BEM, the authors propose a new distribution of boundary source points that removes the singularity from the integrals. This allows the boundary integrals to be precisely calculated using the standard Gaussian quadrature rule with 16 quadrature nodes. Several numerical examples are presented to evaluate the efficiency of the radial BEM compared to standard BEM and RBF collocation method for solving partial differential equations (PDEs). The analytical and numerical studies demonstrate that the radial BEM is a superior version of BEM that will significantly enhance the application of BEM and RBFs in solving PDEs.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"203 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-31DOI: 10.1016/j.amc.2024.129256
Hongpeng Shi, Zhenli Zhao, Shuping Ma
The dissipative control problem for nonlinear discrete-time switched singular systems (NDSSSs) is investigated via a novel reduced-order observer in this paper. Firstly, based on the generalized Sylvester equations and the introduced nonlinear injection term, a novel reduced-order observer is designed for each subsystem. The designed reduced-order observer can still produce accurate full-information estimation even though the dynamics and the output of the systems both contain unknown inputs. Then, by using average dwell-time scheme and multi-Lyapunov functions, some new sufficient conditions are proposed such that the resulted closed-loop NDSSSs are regular and causal, have a unique solution, and are globally uniformly asymptotically stable with a strict (Q,S,V)-γ-dissipative. A novel relaxation technique is proposed for decoupling nonlinear inequalities involving products of multiple nonsquare unknown variables. The design procedures of reduced-order observer and controller are presented by a specific algorithm. Finally, two numerical examples and an electronic circuit example are provided to illustrate the effectiveness of the theoretical results.
{"title":"Reduced-order full information estimation observer-based dissipative control for nonlinear discrete-time switched singular systems with unknown inputs","authors":"Hongpeng Shi, Zhenli Zhao, Shuping Ma","doi":"10.1016/j.amc.2024.129256","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129256","url":null,"abstract":"The dissipative control problem for nonlinear discrete-time switched singular systems (NDSSSs) is investigated via a novel reduced-order observer in this paper. Firstly, based on the generalized Sylvester equations and the introduced nonlinear injection term, a novel reduced-order observer is designed for each subsystem. The designed reduced-order observer can still produce accurate full-information estimation even though the dynamics and the output of the systems both contain unknown inputs. Then, by using average dwell-time scheme and multi-Lyapunov functions, some new sufficient conditions are proposed such that the resulted closed-loop NDSSSs are regular and causal, have a unique solution, and are globally uniformly asymptotically stable with a strict <mml:math altimg=\"si1.svg\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"script\">Q</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"script\">S</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"script\">V</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math>-<ce:italic>γ</ce:italic>-dissipative. A novel relaxation technique is proposed for decoupling nonlinear inequalities involving products of multiple nonsquare unknown variables. The design procedures of reduced-order observer and controller are presented by a specific algorithm. Finally, two numerical examples and an electronic circuit example are provided to illustrate the effectiveness of the theoretical results.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"24 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-30DOI: 10.1016/j.amc.2024.129251
Fangyuan Liu, Guobao Liu, Huai Liu, Shicheng Huo
This paper explores the extended dissipative analysis of integral sliding mode control in the context of singular interval type-2 (IT-2) fuzzy systems with time delays. To better align with the characteristics of type-2 fuzzy models, a suitable integral fuzzy switching surface is introduced, taking into account state-dependent input matrices. Additionally, to address conservatism resulting from time delays, the paper utilizes suitable augmented Lyapunov-Krasovskii functionals and integral inequalities based on auxiliary functions to analyze the system's extended dissipative properties. Furthermore, by leveraging membership function dependency (MFD), this article effectively addresses the premise variable mismatch issue. The paper also provides relaxed stability conditions for feedback system stability and attainability of the desired sliding surface. Finally, the inclusion of illustrative examples serves to validate the efficacy of this approach.
{"title":"Extended dissipative analysis of integral sliding mode control for singular interval type-2 fuzzy systems with time delay","authors":"Fangyuan Liu, Guobao Liu, Huai Liu, Shicheng Huo","doi":"10.1016/j.amc.2024.129251","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129251","url":null,"abstract":"This paper explores the extended dissipative analysis of integral sliding mode control in the context of singular interval type-2 (IT-2) fuzzy systems with time delays. To better align with the characteristics of type-2 fuzzy models, a suitable integral fuzzy switching surface is introduced, taking into account state-dependent input matrices. Additionally, to address conservatism resulting from time delays, the paper utilizes suitable augmented Lyapunov-Krasovskii functionals and integral inequalities based on auxiliary functions to analyze the system's extended dissipative properties. Furthermore, by leveraging membership function dependency (MFD), this article effectively addresses the premise variable mismatch issue. The paper also provides relaxed stability conditions for feedback system stability and attainability of the desired sliding surface. Finally, the inclusion of illustrative examples serves to validate the efficacy of this approach.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"82 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-27DOI: 10.1016/j.amc.2024.129253
Panpan Cheng, Yunshu Gao
Let G be a bipartite graph. In this paper, by constructing two extremal graphs, we completely determine the minimum number of edges of G that guaranteeing the existence of two independent chorded cycles. As a byproduct, our result also implies that G contains two independent cycles of different lengths.
{"title":"Extremal function of two independent chorded cycles in a bipartite graph","authors":"Panpan Cheng, Yunshu Gao","doi":"10.1016/j.amc.2024.129253","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129253","url":null,"abstract":"Let <ce:italic>G</ce:italic> be a bipartite graph. In this paper, by constructing two extremal graphs, we completely determine the minimum number of edges of <ce:italic>G</ce:italic> that guaranteeing the existence of two independent chorded cycles. As a byproduct, our result also implies that <ce:italic>G</ce:italic> contains two independent cycles of different lengths.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"30 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.amc.2024.129255
Yuanyuan Ma, Qiannan Zhang, Leilei Xie
The dynamic interactions of multi-information in online social networks present new challenges for understanding and forecasting information dissemination trends, especially the bounded rational decision-making of users when faced with various information. This article introduces evolutionary game theory to analyze user strategies amidst varying information. By using the Fermi function to calculate the imitation probability of netizens and considering the attractiveness of information and the dual social reinforcement effect, a class of G-SFDFRR multi-information delay propagation models has been established. The propagation threshold is calculated using the next-generation matrix method, and the global asymptotic stability of the system is analyzed using the time-delay Lyapunov function. Empirical analysis based on a Twitter dataset validated the model's effectiveness, showing an improvement in the fitting degree of 38.91 and 19.21 % over the SCIR and SICMR models, respectively. Further quantitative analysis through numerical calculations revealed that evolutionary games can delay the peak of information dissemination and accelerate the decline of rumors, highlighting the key role of strategic interaction in curbing rumor spread. Additionally, regulating the positive and negative social reinforcement effects and propagation probabilities can optimize the effect of rumor refutation, with short-term forced silence measures being more effective than long-term ones.
{"title":"A study on multi-information diffusion model considering dual social reinforcement effect from the perspective of evolutionary game","authors":"Yuanyuan Ma, Qiannan Zhang, Leilei Xie","doi":"10.1016/j.amc.2024.129255","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129255","url":null,"abstract":"The dynamic interactions of multi-information in online social networks present new challenges for understanding and forecasting information dissemination trends, especially the bounded rational decision-making of users when faced with various information. This article introduces evolutionary game theory to analyze user strategies amidst varying information. By using the Fermi function to calculate the imitation probability of netizens and considering the attractiveness of information and the dual social reinforcement effect, a class of G-SF<ce:inf loc=\"post\">D</ce:inf>F<ce:inf loc=\"post\">R</ce:inf>R multi-information delay propagation models has been established. The propagation threshold is calculated using the next-generation matrix method, and the global asymptotic stability of the system is analyzed using the time-delay Lyapunov function. Empirical analysis based on a Twitter dataset validated the model's effectiveness, showing an improvement in the fitting degree of 38.91 and 19.21 % over the SCIR and SICMR models, respectively. Further quantitative analysis through numerical calculations revealed that evolutionary games can delay the peak of information dissemination and accelerate the decline of rumors, highlighting the key role of strategic interaction in curbing rumor spread. Additionally, regulating the positive and negative social reinforcement effects and propagation probabilities can optimize the effect of rumor refutation, with short-term forced silence measures being more effective than long-term ones.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"43 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.amc.2024.129254
Nuno Crokidakis
We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals. Transitions between these states occur at rates designed to capture the complex interactions among students, influenced by factors such as romantic rejection, conflicts with peers and teachers, and other school-related challenges. These interactions can escalate into bullying and violent behavior. The model also incorporates the role of parents and school administrators in mitigating bullying through intervention strategies. The results suggest that bullying can be effectively controlled if anti-bullying programs implemented by schools are sufficiently robust. Additionally, the conditions under which bullying persists are explored.
{"title":"A mathematical model for the bullying dynamics in schools","authors":"Nuno Crokidakis","doi":"10.1016/j.amc.2024.129254","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129254","url":null,"abstract":"We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals. Transitions between these states occur at rates designed to capture the complex interactions among students, influenced by factors such as romantic rejection, conflicts with peers and teachers, and other school-related challenges. These interactions can escalate into bullying and violent behavior. The model also incorporates the role of parents and school administrators in mitigating bullying through intervention strategies. The results suggest that bullying can be effectively controlled if anti-bullying programs implemented by schools are sufficiently robust. Additionally, the conditions under which bullying persists are explored.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"48 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-19DOI: 10.1016/j.amc.2024.129249
Ting Ling, Zhang Li, Minyu Feng, Attila Szolnoki
It is a challenging task to reach global cooperation among self-interested agents, which often requires sophisticated design or usage of incentives. For example, we may apply supervisors or referees who are able to detect and punish selfishness. As a response, defectors may offer bribes for corrupt referees to remain hidden, hence generating a new conflict among supervisors. By using the interdependent network approach, we model the key element of the coevolution between strategy and judgment. In a game layer, agents play public goods game by using one of the two major strategies of a social dilemma. In a monitoring layer, supervisors follow the strategy change and may alter the income of competitors. Fair referees punish defectors while corrupt referees remain silent for a bribe. Importantly, there is a learning process not only among players but also among referees. Our results suggest that large fines and bribes boost the emergence of cooperation by significantly reducing the phase transition threshold between the pure defection state and the mixed solution where competing strategies coexist. Interestingly, the presence of bribes could be as harmful for defectors as the usage of harsh fines. The explanation of this system behavior is based on a strong correlation between cooperators and fair referees, which is cemented via overlapping clusters in both layers.
{"title":"Supervised cooperation on interdependent public goods games","authors":"Ting Ling, Zhang Li, Minyu Feng, Attila Szolnoki","doi":"10.1016/j.amc.2024.129249","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129249","url":null,"abstract":"It is a challenging task to reach global cooperation among self-interested agents, which often requires sophisticated design or usage of incentives. For example, we may apply supervisors or referees who are able to detect and punish selfishness. As a response, defectors may offer bribes for corrupt referees to remain hidden, hence generating a new conflict among supervisors. By using the interdependent network approach, we model the key element of the coevolution between strategy and judgment. In a game layer, agents play public goods game by using one of the two major strategies of a social dilemma. In a monitoring layer, supervisors follow the strategy change and may alter the income of competitors. Fair referees punish defectors while corrupt referees remain silent for a bribe. Importantly, there is a learning process not only among players but also among referees. Our results suggest that large fines and bribes boost the emergence of cooperation by significantly reducing the phase transition threshold between the pure defection state and the mixed solution where competing strategies coexist. Interestingly, the presence of bribes could be as harmful for defectors as the usage of harsh fines. The explanation of this system behavior is based on a strong correlation between cooperators and fair referees, which is cemented via overlapping clusters in both layers.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"148 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-18DOI: 10.1016/j.amc.2024.129250
Zhuochao Tang, Zhuojia Fu, Meng Chen, Leevan Ling
In this paper, we present a novel least-squares formulation of the Generalized Finite Difference Method (GFDM) and utilize its high-order schemes to solve the coupled bulk-surface reaction-diffusion equations. The coupled bulk-surface problems are composed of bulk equations and surface equations and coupled via some Robin-type boundary conditions. For differential operators on curved surfaces, we focus on the extrinsic definition that defines the surface operators using projection operator to tangent spaces of the surface. By utilizing localization and FD data points, the coupled model is discretized as a large sparse system using the LS-GFDM with two sets of arbitrarily distributed points. Compared with the original GFDM, the LS-GFDM brings about the advantage that it gains flexibility to use FD data points at locations different from the unknown nodal solution values. Finally, numerical demonstrations and applications of Turing pattern formations verify the effectiveness and robustness of the proposed method.
{"title":"A novel localized least-squares collocation method for coupled bulk-surface problems","authors":"Zhuochao Tang, Zhuojia Fu, Meng Chen, Leevan Ling","doi":"10.1016/j.amc.2024.129250","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129250","url":null,"abstract":"In this paper, we present a novel least-squares formulation of the Generalized Finite Difference Method (GFDM) and utilize its high-order schemes to solve the coupled bulk-surface reaction-diffusion equations. The coupled bulk-surface problems are composed of bulk equations and surface equations and coupled via some Robin-type boundary conditions. For differential operators on curved surfaces, we focus on the extrinsic definition that defines the surface operators using projection operator to tangent spaces of the surface. By utilizing localization and FD data points, the coupled model is discretized as a large sparse system using the LS-GFDM with two sets of arbitrarily distributed points. Compared with the original GFDM, the LS-GFDM brings about the advantage that it gains flexibility to use FD data points at locations different from the unknown nodal solution values. Finally, numerical demonstrations and applications of Turing pattern formations verify the effectiveness and robustness of the proposed method.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"32 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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