Introduction to modelling and simulation. Definition of System, classification of systems, classification and limitations of mathematical models and its relation to simulation, Methodology of model building
Unit II:
II
15.00
Modelling through differential equation: linear growth and decay models, non linear growth and decay models, Logistic Model, Basic Model relevant to Population dynamics, Modelling through LPP.
Unit III:
III
15.00
Compartment models. : One- Compartment models and Two- Compartment models. Equilibrium solution, Stability analysis, model validity & verification of models (Model V&V).
Unit IV:
IV
15.00
Environment Biology through ordinary differential equation:-SI Model, SIR Model with and without vaccination, Partial differential equation: Fishers equations and traveling wave solution.
Unit V:
V
15.00
Basic concepts of simulation languages, overview of numerical methods used for continuous simulation, Stochastic models, Monte Carlo methods.
Essential Readings:
D. N. P. Murthy, N. W. Page and E. Y. Rodin, Mathematical Modeling, Pergamon Press.
J. N. Kapoor, Mathematical Modeling, Wiley Estern Ltd.
P. Fishwick: Simulation Model Design and Execution, PHI, 1995, ISBN 0-13-098609-7
A. M. Law, W. D. Kelton: Simulation Modeling and Analysis, McGraw-Hill, 1991, ISBN 0-07-100803-9
J. A. Payne, Introduction to Simulation, Programming Techniques and Methods of Analysis, Tata McGraw Hill Publishing Co. Ltd.
F. Charlton, Ordinary Differential and Differential equation, Van Nostarnd.
V.P. Singh: System Modelling & Simulation, New Age International Publishers.
