Introduction to modeling and simulation. Definition of System, classification of systems, classification and limitations of mathematical models and its relation to simulation, Methodology of model building
Modeling through differential equation: linear growth and decay models, non linear growth and decay models, Logistic Model, Basic Model relevant to Population dynamics, modeling through graphs.
Compartment models. : One- Compartment models and Two- Compartment models. Equilibrium solution, Stability analysis, model validity & verification of models (Model V&V).
Mathematical modeling through second order differential equation:-SI Model, SIR Model with and without vaccination, Partial differential equation: mass and momentum balance equations.
Basic concepts of simulation languages, overview of numerical methods used for continuous simulation, Stochastic models, Monte Carlo methods.
1. D. N. P. Murthy, N. W. Page and E. Y. Rodin, Mathematical Modeling, Pergamon Press.
2. J. N. Kapoor, Mathematical Modeling, Wiley Estern Ltd.
3. P. Fishwick: Simulation Model Design and Execution, PHI, 1995, ISBN 0-13-098609-7
1. A. M. Law, W. D. Kelton: Simulation Modeling and Analysis, McGraw-Hill, 1991, ISBN 0-07-100803-9
2. J. A. Payne, Introduction to Simulation, Programming Techniques and Methods of Analysis, Tata McGraw Hill Publishing Co. Ltd.
3. F. Charlton, Ordinary Differential and Differential equation, Van Nostarnd.
4. V.P. Singh: System Modelling & Simulation, New Age International Publishers.
Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/modeling-and-simulation-optional-paper
[2] https://maths.iisuniv.ac.in/academic-year/2016-2017