Advancements And Applications Of Nonstandard Finite Difference Methods
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Advancements and Applications of Nonstandard Finite Difference Methods
A class of dynamically consistent numerical methods are analyzed for general n-dimensional productive-destructive systems (PDS). Using this analysis, a methodology for constructing positive and elementary stable nonstandard numerical methods is established. The nonstandard approach results in qualitatively superior numerical methods when compared to the standard ones. PDS model a wide range of dynamical systems, including ones with biological, chemical and physical interactions. Building upon this, a nonstandard finite difference method for solving autonomous dynamical systems with positive solutions is constructed. The proposed numerical methods are computationally efficient and easy to implement. Several examples are given which show that the numerical results agree with the theoretical results.
Techniques in Mathematical Modelling
"Techniques in Mathematical Modelling" is a comprehensive textbook designed to provide students, researchers, and practitioners with a solid foundation in the principles, techniques, and applications of mathematical modelling. We cover a wide range of topics, from fundamental concepts and analytical techniques to validation methods and emerging trends. Each chapter includes practical examples, case studies, and exercises to reinforce learning and demonstrate real-world applications. Our book emphasizes the interdisciplinary nature of mathematical modelling, with applications in physics, biology, economics, engineering, social sciences, and more. We encourage hands-on learning through practical exercises, simulations, and projects, allowing readers to apply theoretical concepts to real-world scenarios. Additionally, we explore emerging trends and challenges in the field, including advancements in computational techniques, data analytics, and interdisciplinary collaborations. Written in clear and accessible language, "Techniques in Mathematical Modelling" caters to readers with varying levels of mathematical background, making it suitable for undergraduate and graduate students as well as professionals.
Metamaterials And Nanophotonics: Principles, Techniques And Applications
Author: Kosmas L Tsakmakidis
language: en
Publisher: World Scientific
Release Date: 2022-08-11
This monograph is a detailed introduction to the nascent and ever-evolving fields of metamaterials and nanophotonics, with key techniques and applications needed for a comprehensive understanding of these fields all detailed. These include the 'standard' and high-accuracy 'nonstandard' FDTD techniques, finite-difference frequency-domain mode solvers, the transfer matrix method, analytic calculations for dielectric and plasmonic waveguides, dispersion, Maxwell-Bloch and density functional theory, as well as design methods for constructing metamaterials and nanolasers, and quantum plasmonics. The book is intended for final-year undergraduates, as well as postgraduates or active researchers who wish to understand and enter these fields in a 'user-friendly' manner, and who have a basic understanding of and familiarity with electromagnetic theory.