LEADER 04458nam 2200577 450 001 9910788257203321 005 20220819055056.0 010 $a1-4704-1686-7 035 $a(CKB)3150000000020200 035 $a(EBL)3114344 035 $a(SSID)ssj0001266212 035 $a(PQKBManifestationID)11738187 035 $a(PQKBTitleCode)TC0001266212 035 $a(PQKBWorkID)11249889 035 $a(PQKB)10848407 035 $a(MiAaPQ)EBC3114344 035 $a(RPAM)17934149 035 $a(PPN)197102611 035 $a(EXLCZ)993150000000020200 100 $a20150415h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematics of continuous and discrete dynamical systems $eAMS Special Session in Honor of Ronald Mickens's 70th birthday Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, January 9-10, 2013, San Diego, CA /$fAbba B. Gumel, editor 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2014. 210 4$dİ2014 215 $a1 online resource (310 p.) 225 1 $aContemporary mathematics,$v618$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-9862-0 320 $aIncludes bibliographical references at the end of each chapters. 327 $aPreface -- Biographical Summary of Ronald E. Mickens -- Deterministic and Stochastic SIR Epidemic Models with Power Function Transmission and Recovery Rates -- 1. Introduction -- 2. ODE Model -- 3. CTMC Model -- 4. SDE Model -- 5. Computational Results -- 6. Summary -- Acknowledgments -- References -- Evaluating the Cost-Effectiveness of Vaccination Programs -- 1. Introduction -- 2. Background and modeling framework -- 3. Model extensions and future research -- 4. Summary and concluding remarks -- References -- A Simple Two-Patch Epidemiological Model with Allee Effects and Disease-Modified Fitness -- 1. Introduction -- 2. A two-patch SI model -- 3. Endemic states -- 4. The effects of dispersal -- 5. Discussion -- 6. Proofs -- Acknowledgements -- References -- Designing NSFD Methods for Models of Population Interactions -- 1. Introduction -- 2. Definitions and Preliminaries -- 3. PESN methods for systems with hyperbolic equilibria -- 4. PAESN methods for systems with non-hyperbolic equilibria -- 5. Numerical Simulations -- 6. Discussion and Conclusions -- References -- Nonstandard Discretizations of the SIS Epidemiological Model with and without Diffusion -- 1. Introduction -- 2. Qualitative properties of the model -- 3. Nonstandard Runge-Kutta Method for the SIS Model -- 4. NSFD scheme for the SIS model -- 5. NSFD schemes for SIS-Diffusion Model -- 6. Conclusion -- Acknowledgements -- References -- Galerkin-Least Squares Approximations for Delay Differential Equations: Application to a Circadian Rhythm Model -- 1. Introduction -- 2. Galerkin-Least Squares Approximation -- 3. DDE Model for Circadian Rhythm -- 4. Equilibria and Linear Stability Analysis -- 5. Numerical Simulations -- Conclusions -- Acknowledgements -- References -- Exact Finite Difference Schemes -- 1. Introduction -- 2. Exact Finite Difference Schemes for ODEs -- 3. First-order linear system of two equations -- 4. Exact finite difference schemes for some PDEs -- 5. Discussion -- Acknowledgements -- References -- Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator -- 1. Introduction -- 2. The diffusion-free Brusselator system -- 3. Design of NSFD methods -- 6. Conclusions and perspectives. 410 0$aContemporary mathematics,$v618$x0271-4132 606 $aNonlinear oscillations$vCongresses 606 $aDifferential equations$xAsymptotic theory$vCongresses 615 0$aNonlinear oscillations 615 0$aDifferential equations$xAsymptotic theory 676 $a515.392 686 $a34C15$a34D05$a34D20$a34D23$a37M20$a39A28$a39A30$a92B05$2msc 702 $aMickens$b Ronald E.$f1943- 702 $aGumel$b Abba B.$f1966- 712 12$aAMS Special Session in Honor of Ronald Micken's 70th Birthday on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788257203321 996 $aMathematics of continuous and discrete dynamical systems$93855186 997 $aUNINA