Mathematics of Continuous and Discrete Dynamical Systems
About this Title
Abba B. Gumel, University of Manitoba, Winnipeg, Manitoba, Canada, Editor
Publication: Contemporary Mathematics
Publication Year 2014: Volume 618
ISBNs: 978-0-8218-9862-8 (print); 978-1-4704-1686-7 (online)
This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9–10, 2013, in San Diego, CA.
Included are papers on design and analysis of discrete-time and continuous-time dynamical systems arising in the natural and engineering sciences, in particular, the design of robust nonstandard finite-difference methods for solving continuous-time ordinary and partial differential equation models, the analytical and numerical study of models that undergo nonlinear oscillations, as well as the design of deterministic and stochastic models for epidemiological and ecological processes. Some of the specific topics covered in the book include the analysis of deterministic and stochastic SIR-type models, the assessment of cost-effectiveness of vaccination problems, finite-difference methods for oscillatory dynamical systems (including the Schrödinger equation and Brusselator system), the design of exact and elementary stable finite-difference methods, the study of a two-patch model with Allee effects and disease-modified fitness, the study of the delay differential equation model with application to circadian rhythm and the application of some special functions in the solutions of some problems arising in the natural and engineering sciences.
A notable feature of the book is the collection of some relevant open problems, intended to help guide the direction of future research in the area.
Graduate students and research mathematicians interested in dynamical systems, nonlinear oscillations, numerical methods, mathematical biology, and ecology.
Table of Contents
- L. J. S. Allen and E. J. Allen – Deterministic and Stochastic SIR Epidemic Models with Power Function Transmission and Recovery Rates
- Elamin H. Elbasha and Erik J. Dasbach – Evaluating the Cost-Effectiveness of Vaccination Programs
- Yun Kang and Carlos Castillo-Chavez – A Simple Two-Patch Epidemiological Model with Allee Effects and Disease-Modified Fitness
- Dobromir T. Dimitrov and Hristo V. Kojouharov – Designing NSFD Methods for Models of Population Interactions
- Jean M.-S. Lubuma, Eunice W. Mureithi and Yibeltal A. Terefe – Nonstandard Discretizations of the SIS Epidemiological Model with and without Diffusion
- C. P. Vyasarayani and Tamas Kalmar-Nagy – Galerkin-Least Squares Approximations for Delay Differential Equations: Application to a Circadian Rhythm Model
- Lih-Ing W. Roeger – Exact Finite Difference Schemes
- Andrew Kroshko, Oluwaseun Sharomi, Abba B. Gumel and Raymond J. Spiteri – Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator
- Frederick Ira Moxley III, David T. Chuss and Weizhong Dai – An Implicit Generalized Finite-Difference Time-Domain Scheme for Solving Nonlinear Schrödinger Equations
- J. E. Macías-Díaz – A Dynamically Consistent Mickens-Type Discretization of the Hodgkin-Huxley Partial Differential Equation with Non-Polynomial Reaction Law
- Matthias Ehrhardt – Nonstandard Finite Difference Schemes for the Black–Scholes Equation
- L. Cveticanin – An Analytical Method for Truly Nonlinear Oscillators
- P. M. Jordan – A Note on the Lambert $W$-Function: Applications in the Mathematical and Physical Sciences
- Sandra A. Rucker – Leah-Cosine and -Sine Functions: Definitions and Elementary Properties
- Ivana Kovacic – On the Use of Special Functions for Studying Truly Nonlinear Conservative Oscillators
- Ronald E. Mickens – I Wish I Knew How to ...