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Mathematics of continuous and discrete dynamical systems / [edited by] Abba B. Gumel.

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 618Publication details: Providence : American Mathematical Society, c2014.Description: ix, 310 p. : illustrations ; 26 cmISBN:
  • 9780821898628 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Deterministic and stochastic SIR epidemic models with power function transmission and recovery rates by L. J. S. Allen and E. J. Allen-- Evaluating the cost-effectiveness of vaccination programs by E. H. Elbasha and E. J. Dasbach-- A simple two-patch epidemiological model with Allee effects and disease-modified fitness by Y. Kang and C. Castillo-Chavez-- Designing NSFD methods for models of population interactions by D. T. Dimitrov and H. V. Kojouharov-- Nonstandard discretizations of the SIS epidemiological model with and without diffusion by J. M.-S. Lubuma, E. W. Mureithi, and Y. A. Terefe-- Galerkin-least squares approximations for delay differential equations: Application to a circadian rhythm model by C. P. Vyasarayani and T. Kalmar-Nagy-- Exact finite difference schemes by LIH-ING. W. Roeger-- Design and analysis of NSFD methods for the diffusion-free Brusselator by A. Kroshko, O. Sharomi, A. B. Gumel, and R. J. Spiteri-- An implicit generalized finite-difference time-domain scheme for solving nonlinear Schrodinger equations by F. I. Moxley III, D. T. Chuss, and W. Dai-- A dynamically consistent Mickens-type discretization of the Hodgkin-Huxley partial differential equation with non-polynomial reaction law by J. E. Macias-Diaz-- Nonstandard finite difference schemes for the Black-Scholes equation by M. Ehrhardt-- An analytical method for truly nonlinear oscillators by L. Cveticanin-- A note on the Lambert $W$-function: Applications in the mathematical and physical sciences by P. M. Jordan-- Leah-cosine and -sine functions: Definitions and elementary properties by S. A. Rucker-- On the use of special functions for studying truly nonlinear conservative oscillators by I. Kovacic-- I wish I knew how to... by R. E. Mickens.
Summary: 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 Schrodinger 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.
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Includes bibliographical references.

Deterministic and stochastic SIR epidemic models with power function transmission and recovery rates by L. J. S. Allen and E. J. Allen--
Evaluating the cost-effectiveness of vaccination programs by E. H. Elbasha and E. J. Dasbach--
A simple two-patch epidemiological model with Allee effects and disease-modified fitness by Y. Kang and C. Castillo-Chavez--
Designing NSFD methods for models of population interactions by D. T. Dimitrov and H. V. Kojouharov--
Nonstandard discretizations of the SIS epidemiological model with and without diffusion by J. M.-S. Lubuma, E. W. Mureithi, and Y. A. Terefe--
Galerkin-least squares approximations for delay differential equations: Application to a circadian rhythm model by C. P. Vyasarayani and T. Kalmar-Nagy--
Exact finite difference schemes by LIH-ING. W. Roeger--
Design and analysis of NSFD methods for the diffusion-free Brusselator by A. Kroshko, O. Sharomi, A. B. Gumel, and R. J. Spiteri--
An implicit generalized finite-difference time-domain scheme for solving nonlinear Schrodinger equations by F. I. Moxley III, D. T. Chuss, and W. Dai--
A dynamically consistent Mickens-type discretization of the Hodgkin-Huxley partial differential equation with non-polynomial reaction law by J. E. Macias-Diaz--
Nonstandard finite difference schemes for the Black-Scholes equation by M. Ehrhardt--
An analytical method for truly nonlinear oscillators by L. Cveticanin--
A note on the Lambert $W$-function: Applications in the mathematical and physical sciences by P. M. Jordan-- Leah-cosine and -sine functions: Definitions and elementary properties by S. A. Rucker--
On the use of special functions for studying truly nonlinear conservative oscillators by I. Kovacic--
I wish I knew how to... by R. E. Mickens.

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 Schrodinger 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.

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