NSF-CBMS Regional Research Conference, Nonstandard Finite Difference Methods: Advances in Theory and Applications

该国家科学基金会奖支持2020年NSF-CBMS会议“非标准有限差分方法：理论与应用进展”，该会议将于2020年7月20日至24日在北卡罗来纳a&t州立大学举行。为期5天的会议将邀请克拉克亚特兰大大学的Ronald E. Mickens教授，他将就该主题发表10次讲座，从该方法的基本数值动机开始，包括理论阐述和在科学，医学和工程中不同现象的微分方程模型的各种应用，并以开放问题结束。虽然会议的总体科学目标是理解和扩展非标准有限差分方法（NSFD）方法，这些方法将从讲座和讨论环节中出现，但人类发展目标是介绍和鼓励新的研究人员进入这一令人兴奋的研究领域，重点是来自传统黑人学院和大学以及少数民族服务机构的教师和学生，他们的活动通常仅限于教学。会议旨在激发人们对NSFD方法及其应用研究的兴趣和活动，通过由邀请的高级研究人员主持的实践活动和小组讨论，讨论NSFD模型在应用中的应用，研究生和本科生的研究项目，以及未来合作的框架。主要的会议讲座旨在促进理解和探索NSFD理论和方法应用的新领域，该方法解决了标准有限差分模型中普遍存在的数值不稳定性和人为混沌行为的出现。讲座将从对DEs数值方法的需求开始，向参与者介绍NSFD方法的基本基础和公式，讨论理论和应用的最新进展，总结该领域的开放性问题和可能的未来方向。在理论方面的进展将包括对一般、部分、延迟和分数阶微分方程系统的广义非NSFD构造方法的潜在变革概念的探索。在应用方面的进展将突出与各种研究的工程，科学，和经典的或新兴的兴趣数学现象由各种类型的微分方程建模。Mickens教授的讲座将整合成专著，将这些不同的研究领域统一起来，并将作为促进数学科学和其他科学与工程学科的理解、发现和跨学科合作的资源。进一步的会议信息可在http://www.ncat.edu/~math/cbms2020/This上获得，奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This National Science Foundation award supports the 2020 NSF-CBMS conference "Nonstandard Finite Difference Methods: Advances in Theory and Applications" to be held July 20-24, 2020 at North Carolina A&T State University. The 5-day conference will feature Professor Ronald E. Mickens of Clark Atlanta University, who will deliver ten lectures on the topic, beginning with basic numerical motivations for the method, including theoretical exposition and various applications to differential equations models of diverse phenomena in the sciences, medicine, and engineering, and concluding with open problems. While the general scientific goal of the conference is the understanding and extensions of nonstandard finite difference methods (NSFD) methods that will emerge from the lectures and the discussion sessions, the human development goal is to introduce and encourage new researchers to this exciting field of research, with a focus on faculty and students from Historically Black Colleges and Universities and Minority Serving Institutes, whose activities are normally confined to teaching. The conference is intended to stimulate interest and activity in the study of NSFD methods and their applications, to be enabled by hands-on activities as well as panel discussions led by invited senior researchers on NSFD models in applications, graduate and undergraduate research projects, and a framework for future collaborations.The main conference lectures are designed to advance understanding and explore new frontiers in NSFD theory and applications of the methodology, which addresses the emergence of numerical instabilities and contrived chaotic behavior that is prevalent in standard finite difference models. Beginning with need for numerical methods for DEs, the lectures will introduce participants to the basic foundations and formulations of the NSFD methodology, discuss the state-of-the-art and latest advances in theory and applications, and summarize open problems as well as possible future directions in the field. Advances in theory will include explorations of potentially transformative concepts for generalized NSFD construction methods for systems of ordinary, partial, delay, and fractional differential equations. Advances in applications will be highlighted with various studies of engineering, science, and mathematical phenomena of classic or emerging interest modeled by the various classes of differential equations. The lectures presented by Professor Mickens, to be consolidated in a monograph, will unify these disparate research areas at their intersection and will serve as a resource to advance understanding, discovery, and inter-disciplinary collaboration in the mathematical sciences and other science and engineering disciplines. Further conference information will be available at http://www.ncat.edu/~math/cbms2020/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.