作者机构：
[Chen, Bizhong; Yao, Liangshuang] Minist Educ, Key Lab Adolescent Cyberpsychol & Behav CCNU, Wuhan, Peoples R China.;[Sun, Xiaojun] Cent China Normal Univ, Sch Psychol, Wuhan, Peoples R China.;[Huang, Xuan] Beijing Normal Univ, Fac Psychol, Beijing, Peoples R China.;[Sun, Xiaojun; Sun, XJ] Cent China Normal Univ CCNU, Sch Psychol, 382 Xiongchu Rd, Wuhan 430079, Peoples R China.
通讯机构：
[Sun, XJ ] C;Cent China Normal Univ CCNU, Sch Psychol, 382 Xiongchu Rd, Wuhan 430079, Peoples R China.
关键词：
social anxiety;social relationships;longitudinal studies;meta-analysis
摘要：
It is theoretically plausible that social anxiety (SA) and social relationships (SR) can influence each other. However, the available empirical evidence is inconsistent, leading to substantial uncertainty regarding the cross-lagged relations between SA and SR. This meta-analysis systematically integrates data from 107 longitudinal studies, comprising 110 independent samples and involving a total of 115,133 participants from childhood to adulthood. Four types of SR were assessed: family-related, school-related, romantic, and general relationships. One-stage meta-analytic structural equation modeling was applied to fit four cross-lagged panel models and to test potential moderators. No significant publication bias was detected. Effect size analyses revealed that prior SA significantly and negatively predicted quality of all types of SR. Family-related and general relationships each predicted prospective SA symptoms, but school-related and romantic relationships did not. No moderators were identified in analyses of family-related and romantic relationships. However, the publication year, sample age, gender, reporter, and time lag played a moderating role in analyses of school-related and general relationships. These findings suggest that SA is a crucial factor undermining SR and that dysfunctional family and general relationships also contribute to the exacerbation of SA symptoms. The strengths, limitations, and future directions of this study are discussed. Public Significance Statement A hotly debated issue in academia is whether past social anxiety (SA) hinders future social relationships(SR) or if prior poor SR precipitate subsequent SA symptoms. To shed light on this matter, a comprehensive meta-analysis was conducted, encompassing data from 107 longitudinal studies and involving over 110,000 participants. The findings suggest that SA poses a significant risk to all types of SR, but only family-related and general relationships potentially impacted later levels of SA.
作者：
Li, Jiayuan;Bai, Jie;Zhu, Sha;Yang, Harrison Hao
期刊：
Electronics,2024年13(2):385- ISSN：2079-9292
通讯作者：
Zhu, S;Yang, HH
作者机构：
[Zhu, Sha; Zhu, S; Bai, Jie; Li, Jiayuan] Cent China Normal Univ, Natl Engn Res Ctr E Learning, Wuhan 430079, Peoples R China.;[Yang, HH; Yang, Harrison Hao] SUNY Coll Oswego, Sch Educ, Oswego, NY 13126 USA.
通讯机构：
[Yang, HH ] S;[Zhu, S ] C;Cent China Normal Univ, Natl Engn Res Ctr E Learning, Wuhan 430079, Peoples R China.;SUNY Coll Oswego, Sch Educ, Oswego, NY 13126 USA.
关键词：
digital literacy;digital game-based assessment;ECGD;AHP;assessment model
摘要：
This study measured secondary students' digital literacy using a digital game-based assessment system that was designed and developed based on the Evidence-Centered Game Design (ECGD) approach. A total of 188 secondary students constituted the valid cases in this study. Fine-grained behavioral data generated from students' gameplay processes were collected and recorded with the assessment system. The Delphi method was used to extract feature variables related to digital literacy from the process data, and the Analytic Hierarchy Process (AHP) method was used to construct the measurement model. The assessment results of the ECGD-based assessment had a high correlation with standardized test scores, which have been shown to be reliable and valid in prior large-scale assessment studies.
期刊：
Pesticide Biochemistry and Physiology,2024年199:105769 ISSN：0048-3575
通讯作者：
Sun, Y;Zhang, AD
作者机构：
[Zhou, Yaqing; Wang, Jili; Sun, Yong; Sun, Y; Zhou, Xin; Wu, Wenhai] Hanjiang Normal Univ, Coll Chem & Environm Engn, Shiyan 442000, Peoples R China.;[Zhang, Aidong; Han, Mengying] Cent China Normal Univ, Coll Chem, Natl Key Lab Green Pesticide, Wuhan 430079, Peoples R China.
通讯机构：
[Zhang, AD ] C;[Sun, Y ] H;Hanjiang Normal Univ, Coll Chem & Environm Engn, Shiyan 442000, Peoples R China.;Cent China Normal Univ, Coll Chem, Natl Key Lab Green Pesticide, Wuhan 430079, Peoples R China.
摘要：
The discovery of safe, effective, and selective chemical algicides is the stringent need for the algicides development, and it is also one of the effective routes to control cyanobacteria harmful algal blooms and to meet the higher requirements of environmental and ecological. In this work, a series of novel bromo-N-phenyl-5-ohydroxyphenylpyrazole-3-carboxyamides were rationally designed as pseudilin analogs by bioisosteric replacement and molecular hybridization strategies, in which the pyrrole unit of pseudilin was replaced with pyrazole and further combined with the dominant structural fragments of algicide diuron. The synthesis was carried out by a facile four-step routeincluding cyclization, amidation, transanulation, and halogenation. The biological activity evaluation on AtIspD, EcIspD, Synechocystis sp. PCC6803 and Microcystis aeruginosa FACHB905 revealed that most compounds had good EcIspD and excellent cyanobacteria inhibitory activity. In particular, compound 6bb exhibited potent algicidal activity against PCC6803 and FACHB905 with EC50 = 1.28 mu M and 0.37 mu M, respectively, 1.4-fold and 4.0-fold enhancement compared to copper sulfate (EC50 = 1.79 and 1.49 mu M, respectively), and it also showed the best inhibitory activity of EcIspD. The binding of 6bb to EcIspD was explored by molecular docking, and it was confirmed that 6bb could bind to the EcIspD active site. Compound 6bb was proven to be a potential structure for the further development of novel algicides that targets IspD in the MEP pathway.
关键词：
Social network sites use;Depression;Self-esteem;Self-compassion;Children
摘要：
Previous research has conducted extensive work on the impact of social network site (SNS) use on depression. However, most of these studies have focused on adolescents or adults, and little is known about how SNS use affects depression among children. Based on the vulnerability model of depression, the self-system beliefs model, and the risk-buffering hypothesis, we examined whether self-esteem would mediate the relationship between SNS use and children's depression and whether self-compassion would play a moderating role in the mediating process. The sample consisted of 386 Chinese children from grades three to six (Mage = 9.83 years, SD = 1.23; 42.5 % girls), who provided self-reported data on demographic variables, SNS use, self-esteem, depression, and self-compassion. Results indicated that after controlling for the children's gender and age, the partial mediating role of self-esteem between SNS use and depression was significant at low levels of self-compassion, marginally significant at high levels, and non-significant at mean levels. Moreover, both the first and second stages of the indirect effects were moderated by self-compassion. Specifically, the effects of SNS use on self-esteem were negative, non-significant, and marginally positive for children with low, middle, and high self-compassion, respectively. The interaction pattern of self-esteem and self-compassion on depression fit the protective-attenuating hypothesis: the protective effect of self-compassion was stronger for children with low self-esteem. This study extends our understanding of the underlying mechanisms linking SNS use to depression among children, which has both theoretical and practical implications for interventions for children's depressive symptoms. The limitations and theoretical and practical implications of this study are discussed.
作者机构：
[Wen, S P; Hou, G Y; Li, Xiaoyu; Liang, H; Dai, H L; Yuan, C Z; Zhao, G; Xu, W; Xiao, S Y; Zhao, Ling; Ma, Q M; Lou, X C; Hou, X T; Zhang, P; Liu, K; Tang, G Y; Batozskaya, V; Liu, P L; Wang, H P; Cao, G F; Sun, H K; Yan, X Q; Wang, Y F; Zhang, Jiawei; Kiuchi, R; Shi, R S; Wang, Y Q; Sun, Y Z; Zhang, J Z; Zhang, J W; Zhang, J Y; Zhang, Z H; Wang, Yaqian; K, X; Liu, C X; Mo, X H; Hu, Y; Hu, T; Song, W M; Zhu, Z A; Wu, Z; Zheng, W J; Chang, J F; Yuan, Y; Deng, Z Y; Yang, Yifan; Lu, J G; Yu, G; Hu, H M; Zheng, J P; Zeng, Y J; Ma, R Q; Ouyang, Q; Fang, W X; Liu, Huanhuan; Chen, T; Yuan, S C; Fu, Y W; Rong, G; Chen, G; Ding, B; Liu, B J; Zhu, K J; Hou, Z L; Ablikim, M; Xu, C F; Cai, X; Li, L K; Yang, Tao; Li, L J; Ma, H L; Qiu, J F; Zhang, Shuihan; Liu, Fang; Ma, X Y; Lu, Y P; Heng, Y K; Chang, W L; Qin, Z H; Fang, S S; Wang, B; Sun, S S; Wang, K; Ping, R G; Du, M C; Wang, Z; Liu, H M; Liao, Y P; Mao, Z P; Yin, J H; Yu, B X; Gong, W X; Lu, Z H; Chen, M L; Li, Ke; Zhu, K; Ji, X L; Zhang, B X; Ji, X B; Zhang, B L; Guan, C Y; Jing, M Q; Li, G; Shi, J Y; Li, F; Lin, T; Yuan, X Q; Zhang, A Q; Li, H B; Lu, X L; Xu, G F; Chen, X T; Yang, H X; Gu, M H; Zhang, Yao; Wang, Z Y; Zhang, Y H; Zou, J H; Wu, L H; Wu, L J; Zhang, H Q; Zhou, L P; Chen, H S; Shao, L G; Fu, C D; Zhao, J Y; Zhao, J Z; Xing, T Y; Li, W D; Li, W G; He, K L; Ma, M M; Qi, F Z; Qian, S; Yang, Y X; Zhang, X M; Zhang, H Y; Zhao, Y B; Chen, Y B; Sun, G X; Wang, L L; Ning, Z; Huang, Y P; Wang, Meng; Ma, J L; Dong, L Y; Luo, X L; Jiang, X S; Fang, Y; Fang, J; Ye, M; Shen, X Y; Dong, M Y; Cao, N; Miao, H; Shi, X; Ji, Q; Wu, J F; Liu, Z A; Shen, H F; Sun, T; Xie, Y G; Dong, J; Liu, J Y] Institute of High Energy Physics, Beijing 100049, People's Republic of China;[Achasov, M N; Muchnoi, N Yu; Nikolaev, I B] Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia;[Adlarson, P; Schoenning, K; Thoren, V; Kupsc, A; Wolke, M; Johansson, T] Uppsala University, Box 516, SE-75120 Uppsala, Sweden;[Li, D M; Liu, Y; Zhang, J; Du, S X; Yan, W C; Zhang, Q Y; Ai, X C; Zhao, S J; Ke, B C; Zhang, Y T] Zhengzhou University, Zhengzhou 450001, People's Republic of China;[Redmer, C F; Hüsken, N; Schelhaas, Y; Lenz, T; Lellmann, M; Stieler, F; Leithoff, H; Muskalla, J; Gradl, W; Aliberti, R; Heinz, C H; Plura, S; Berger, N; Denig, A] Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
摘要：
Based on data samples collected with the BESIII detector at the BEPCII collider, the process e^{+}e^{-}→Σ^{+}Σ[over ¯]^{-} is studied at center-of-mass energies sqrt[s]=2.3960, 2.6454, and 2.9000GeV. Using a fully differential angular description of the final state particles, both the relative magnitude and phase information of the Σ^{+} electromagnetic form factors in the timelike region are extracted. The relative phase between the electric and magnetic form factors is determined to be sinΔΦ=-0.67±0.29(stat)±0.18(syst) at sqrt[s]=2.3960 GeV, ΔΦ=55°±19°(stat)±14°(syst) at sqrt[s]=2.6454 GeV, and 78°±22°(stat)±9°(syst) at sqrt[s]=2.9000 GeV. For the first time, the phase of the hyperon electromagnetic form factors is explored in a wide range of four-momentum transfer. The evolution of the phase along with four-momentum transfer is an important input for understanding its asymptotic behavior and the dynamics of baryons.
作者机构：
[Huang, Jing] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China.;[Geng, Xianya] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan, Peoples R China.;[Zhou, Zihan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Zhou, Zihan] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
通讯机构：
[Zhou, ZH ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
摘要：
Identifying the graph with maximum or minimum spectral radius among a given class of graphs is a central problem in extremal spectral graph theory, known as the Brualdi- Solheid problem. For a graph G = (V-G, E-G), a subset S subset of V-G is called a maximum dissociation set if the induced subgraph G[S] does not contain P-3 as its subgraph, and the subset has maximum cardinality. The dissociation number of G is the number of vertices in a maximum dissociation set of G. In this paper, we first characterize all the connected graphs (resp. bipartite graphs, trees) having maximum spectral radius among connected graphs (resp. bipartite graphs, trees) with given order and dissociation number. Secondly, we show that the connected n-vertex graph with dissociation number phi having minimum spectral radius is a tree, where phi >= [2/3n] . Finally, we determine the graphs having minimum spectral radius with fixed order n and dissociation number phi is an element of {2, [2n/3], n - 1, n - 2}.(c) 2023 Elsevier B.V. All rights reserved.
摘要：
With the proliferation of social media, the detection of fake news has become a critical issue that poses a significant threat to society. The dissemination of fake information can lead to social harm and damage the credibility of information. To address this issue, deep learning has emerged as a promising approach, especially with the development of Natural Language Processing (NLP). This study introduces a novel approach called Graph Global Attention Network with Memory (GANM) for detecting fake news. This approach leverages NLP techniques to encode nodes with news context and user content. It employs three graph convolutional networks to extract informative features from the news propagation network and aggregates endogenous and exogenous user information. This methodology aims to address the challenge of identifying fake news within the context of social media. Innovatively, the GANM combines two strategies. First, a novel global attention mechanism with memory is employed in the GANM to learn the structural homogeneity of news propagation networks, which is the attention mechanism of a single graph with a history of all graphs. Second, we design a module for partial key information learning aggregation to emphasize the acquisition of partial key information in the graph and merge node-level embeddings with graph-level embeddings into fine-grained joint information. Our proposed method provides a new direction in news detection research with a combination of global and partial information and achieves promising performance on real-world datasets.
作者机构：
[Huan Yang; Yajun Guo] School of Computer Science, Central China Normal University, Wuhan, 430079, Hubei, China;[Yimin Guo] School of Information and Safety Engineering, Zhongnan University of Economics and Law, Wuhan, 430073, Hubei, China
通讯机构：
[Yajun Guo] S;School of Computer Science, Central China Normal University, Wuhan, 430079, Hubei, China
摘要：
With the rapid development of IoT technology, smart homes have emerged. At the same time, data security and privacy protection are also of great concern. However, the traditional centralized authentication scheme has defects such as single point of failure, poor scalability, center dependence, vulnerability to attacks, etc., and is not suitable for the distributed and dynamically changing smart home environment. Thus, many researchers have proposed decentralized authentication schemes based on blockchain technology. Although many characteristics of blockchain technology such as decentralization, non-tampering, and solving single point of failure have good application scenarios in authentication, the mature integration of the two applications has to be further explored. For example, the introduction of blockchain also brings security issues; the balance between security and performance in most blockchain-based authentication schemes remains to be investigated; and resource-constrained IoT devices tend to perform a large number of intensive computations, which is clearly inappropriate. Consequently, this paper introduces fog computing in blockchain-based authentication schemes, proposes a network architecture in which cloud and fog computing work together, and investigates the security and performance issues of authentication schemes under this architecture. Finally, formal and informal security analysis show that our scheme has multiple security properties, and our scheme has better performance than existing solutions.
期刊：
Educational Research Review,2024年43:100591 ISSN：1747-938X
通讯作者：
Huanyou Chai
作者机构：
[Tianhui Hu] Faculty of Artificial Intelligence in Education, Central China Normal University, Wuhan, 430079, Hubei, China;Research Center of Distance Education, Beijing Normal University, Beijing, 100875, China;[Li Wu] School of Education, Central China Normal University, Wuhan, 430079, Hubei, China;[Huanyou Chai] Faculty of Artificial Intelligence in Education, Central China Normal University, Wuhan, 430079, Hubei, China<&wdkj&>Research Center of Distance Education, Beijing Normal University, Beijing, 100875, China
通讯机构：
[Huanyou Chai] F;Faculty of Artificial Intelligence in Education, Central China Normal University, Wuhan, 430079, Hubei, China<&wdkj&>Research Center of Distance Education, Beijing Normal University, Beijing, 100875, China
摘要：
Given the widespread concern on collaborative problem solving (CPS) skills, there has been an increasing interest in the last few years to explore how to assess them with digital technologies. This study systematically reviewed how CPS skills have been assessed with digital technologies in the literature. A total of 40 articles were reviewed to analyze specific computer-based assessment instruments of CPS skills from four perspectives: research context, theoretical model for assessment, assessment type, and reliability and validity evidence. The results indicate that most tests target a sample of less than 500 junior students. Nine theoretical models are employed for assessing CPS skills, most of which treat these skills as an explicit combination of social and cognitive skills and are applied to a limited range of participants' age levels, collaboration features, and team compositions. A total of 22 tests have been employed and fallen into four types, i.e., the ones with specific predefined messages in human-agent mode, and those with online chat box, videoconferencing, and face-to-face collaboration in human-human mode. Each type of these tests demonstrates great diversities in participants’ age levels, types of CPS task(s), team compositions, types of assessment data, and methods of data recording and scoring. A certain number of tests lack reliability and validity evidence. Our findings are expected to benefit relevant researchers and test developers in terms of providing suggestions for future research which include testing the applicability of theoretical models for assessing CPS skills across a wide range of assessment contexts. In addition, future researchers should improve the development, data processing, and report of those four types of computer-based assessment instruments of CPS skills through different approaches, respectively.
作者机构：
[Zhang, Xian; Zhang, Ruiping] The Radiology Department of First Hospital of Shanxi Medical University, Taiyuan, 030001, P. R. China;[Zhang, Xian; Dou, You; Li, Junrong; Sun, Yao] National Key Laboratory of Green Pesticides, International Joint Research Center for Intelligent Biosensor Technology and Health, College of Chemistry, Central China Normal University, Wuhan, Hubei, 430079, P. R. China;[Liu, Shuang] School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China;[Chen, Peiyao] Key Laboratory of Fermentation Engineering (Ministry of Education), National "111" Center for Cellular Regulation and Molecular Pharmaceutics, Hubei Key Laboratory of Industrial Microbiology, School of Food and Biological Engineering, Hubei University of Technology, Wuhan, 430068, China;[Wen, Yating] Shanxi Bethune Hospital, Shanxi Academy of Medical Sciences, Tongji Shanxi Hospital, Third Hospital of Shanxi Medical University, Taiyuan, 030001, P. R. China
摘要：
Although being applied as photosensitizers for photodynamic therapy, covalent organic frameworks (COFs) fail the precise fluorescence imaging in vivo and phototherapy in deep-tissue, due to short excitation/emission wavelengths. Herein, we propose the first example of NIR-II emissive and benzobisthiadiazole-based COF-980. Comparing to its ligands, the structure of COF-980 could more efficiently reducing the energy gap (ΔE(S1-T1) ) between the excited state and the triplet state to enhance photodynamic therapy efficiency. Importantly, COF-980 demonstrates high photostability, good anti-diffusion property, superior ROS generation efficiency, promising imaging ability and ROS production in deep tissue (ཞ8mm). In vitro results reveal COF-980 combined with laser irradiation could trigger larger amount of intracellular ROS to high-efficiently induce cancer cell death. Notably, COF-980 NPs precisely enables PDT guided by NIR-II fluorescence imaging that effectively inhibit the 4T1 tumor growth with negligible adverse effects. This study provides a universal approach to developing long-wavelength emissive COFs and exploits its applications for biomedicine. This article is protected by copyright. All rights reserved.
期刊：
FRONTIERS IN PSYCHOLOGY,2024年15:1288644 ISSN：1664-1078
作者机构：
Key Laboratory of Adolescent Cyberpsychology and Behavior (CCNU), Ministry of Education, China;School of Fundamental Education, South China Normal University, China
摘要：
Whether parental educational expectations for adolescents serve as a source of motivation or stress depends on the extent to which adolescents hold expectations for themselves. Previous research on the discrepancies between parental and adolescent educational expectations and their impact on learning engagement has been limited by traditional statistical tests, and lacking an examination of the internal mediating mechanism of parent–child relational quality from both parental and adolescent perspectives. This cross-sectional study, utilizing a multi-informant design, examined the association between discrepancies in parents’ and adolescents’ reports of expectations, and adolescents’ study engagement, as well as the mediating role of parent–child relational qualities perceived by both parties. The sample for this study consisted of 455 adolescents and their parents from 10 classes in a junior high school in Wuhan, Hubei Province, China. The adolescents had an average age of 12.8 years, and 51.6% of them were boys. Both parents and adolescents reported on their expectations and perceived relational quality, while adolescents also filled out questionnaires assessing their learning engagement. Data were analyzed using polynomial regressions with response surface analysis. The results revealed that when adolescents reported high expectations, regardless of whether their parents reported high or low expectations, adolescents reported satisfied relationships and high learning engagement. In contrast, parents reported satisfied relationships when both parties reported high expectations, or when parents reported higher expectations than adolescents. Lastly, the association between discrepancies in expectations and learning engagement was significantly mediated by adolescent-reported relationships but not parent-reported ones. These findings highlight the importance of considering multiple perspectives when studying the association between expectations and adolescent study engagement. This research advances our comprehension of the dynamics between parent-adolescent educational expectation discrepancies and adolescent learning engagement, offering insights for more nuanced and effective parenting strategies tailored to foster optimal educational outcomes.
摘要：
Accurately predicting hydrological runoff is crucial for water resource allocation and power station scheduling. However, there is no perfect model that can accurately predict future runoff. In this paper, a daily runoff prediction method with a seasonal decomposition-based-deep gated-recurrent-unit (GRU) method (SD-GRU) is proposed. The raw data is preprocessed and then decomposed into trend, seasonal, and residual components using the seasonal decomposition algorithm. The deep GRU model is then used to predict each subcomponent, which is then integrated into the final prediction results. In particular, the hyperparameter optimization algorithm of tree-structured parzen estimators (TPE) is used to optimize the model. Moreover, this paper introduces the single machine learning model (including multiple linear regression (MLR), back propagation (BP), long short-term memory neural network (LSTM) and gate recurrent unit (GRU)) and a combination model (including seasonal decomposition–back propagation (SD-BP), seasonal decomposition–multiple linear regression (SD-MLR), along with seasonal decomposition–long-and-short-term-memory neural network (SD-LSTM), which are used as comparison models to verify the excellent prediction performance of the proposed model. Finally, a case study of the Qingjiang Shuibuya test set, which considers the period 1 January 2019 to 31 December 2019, is conducted. Case studies of the Qingjiang River show the proposed model outperformed the other models in prediction performance. The model achieved a mean absolute error (MAE) index of 38.5, a Nash-Sutcliffe efficiency (NSE) index of 0.93, and a coefficient of determination (R2) index of 0.7. In addition, compared to the comparison model, the NSE index of the proposed model increased by 19.2%, 19.2%, 16.3%, 16.3%, 2.2%, 2.2%, and 1.1%, when compared to BP, MLR, LSTM, GRU, SD-BP, SD-MLR, SD-LSTM, and SD-GRU, respectively. This research can provide an essential reference for the study of daily runoff prediction models.
作者：
He, Ying;Wang, Yan;Yang, Jerry Zhijian;Yin, Hongshuang
期刊：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2024年14(1):79-103 ISSN：2079-7362
通讯作者：
Wang, Y
作者机构：
[Yang, Jerry Zhijian; Yin, Hongshuang; He, Ying] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[He, Ying] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Global Science Press;EAJAM;East Asian Journal on Applied Mathematics;Nonlinear Dirac equation;uniformly accurate;finite difference method;time-splitting method;exponential integrator.
摘要：
Numerical methods for the nonlinear Dirac equation (NDE) in the massless nonrelativistic regime are considered. In this regime, the equation contains a small dimensionless parameter $0 <\varepsilon≤ 1,$ and its solution is highly oscillatory in time. We present and analyze traditional numerical schemes for the NDE, including finite difference methods, time-splitting methods and exponential integrators. Error analysis indicates that all these methods require an $\varepsilon$-dependent time-step size to achieve an optimal convergence order. Utilizing an operator splitting technique, we propose a uniformly accurate (UA) scheme. The scheme enables first-order convergence in time for all $\varepsilon ∈ (0, 1]$ without restrictions on time-step size. Error estimates for the UA scheme are rigorously established and numerical results confirm the properties of the method.
