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

该国家科学基金奖支持将于2020年7月20-24日在北卡罗来纳农工大学举行的2020年NSF-CBMS“非标准有限差分方法：理论和应用进展”会议。为期5天的会议将由克拉克·亚特兰大大学的罗纳德·E·米肯斯教授主持，他将就这一主题发表10场演讲，从该方法的基本数值动机开始，包括理论阐述和对科学、医学和工程中不同现象的微分方程模型的各种应用，最后以开放问题结束。虽然会议的总体科学目标是理解和推广讲座和讨论中出现的非标准有限差分法(NSFD)方法，但人类发展的目标是向这一令人兴奋的研究领域介绍和鼓励新的研究人员，重点是来自历史悠久的黑人学院和少数民族服务学院的教职员工和学生，他们的活动通常仅限于教学。这次会议的目的是激发人们对NSFD方法及其应用的研究兴趣和活力，通过实际操作活动以及由受邀的高级研究人员领导的小组讨论，在应用、研究生和本科生研究项目以及未来合作的框架下进行NSFD模型的研究。主要会议讲座旨在促进对NSFD理论和方法应用的新前沿的理解和探索，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DES对数值方法的需求开始，向与会者介绍NSFD方法的基本基础和公式，讨论理论和应用方面的最新进展和最新进展，并总结该领域的公开问题和可能的未来方向。在理论上的进展将包括对常微分方程组、偏微分方程组、延迟微分方程组和分数阶微分方程组的广义NSFD构造方法的潜在变革性概念的探索。应用方面的进步将突出各种工程、科学和数学现象的研究，这些现象是经典的或新兴的，由各种类型的微分方程式建模。米肯斯教授的演讲将合并成一本专著，将统一这些相交的不同研究领域，并将作为一种资源，促进在数学科学和其他科学和工程学科中的理解、发现和跨学科合作。更多的会议信息将在http://www.ncat.edu/~math/cbms2020/This颁奖典礼上公布，该奖项反映了国家科学基金会的法定使命，并已通过使用基金会的智力优势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.