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Mathematics
Numerical Solution of Ordinary and Partial Differential Equations (Web)
Syllabus
Co-ordinated by :
IIT Roorkee
Available from :
2012-08-17
Lec :
1
Modules / Lectures
Numerical Solution of Ordinary Differential Equations
Numerical solution of first order ordinary differential equations
Numerical Methods: Euler method
Modified Euler Method
Runge Kutta Method
Fourth Order Runge Kutta Methods
Higher order Runge Kutta Methods
Multi-step methods
Multi Step Methods Predictor corrector Methods
Multi Step Methods Predictor corrector Methods Contd…
Multi Step Methods Adams Bashforth method
Multi Step Methods Adams Moulton method
Systems of equations and higher order equations
Systems of Differential Equations
Higher Order Equations
Stiff Differential equations
Linear Boundary value problems
Finite Difference Methods: Dirichlet type boundary condition
Finite Difference Methods: Mixed boundary condition
Shooting Method
Shooting Method contd…
Non-linear Boundary value problems
Solution by Finite Difference Methods
Shooting Methods
Shooting Methods Contd…
Numerical Solution of Partial Differential Equations
Introduction of PDE, Classification and Various type of conditions
Finite Difference representation of various Derivatives
Explicit Method for Solving Parabolic PDE
Parabolic Partial Differential Equations : One dimensional equation : Explicit method.
Crank Nicolson method and Fully Implicit method
Three Time Level Schemes
Extension to 2d Parabolic Partial Differential Equations
Compatibility of one-dimensional Parabolic PDE
Compatibility and Stability of 1d Parabolic PDE
Stability of one-dimensional Parabolic PDE
Convergence of one?dimensional Parabolic PDE
Elliptic Partial Differential Equations
Elliptic Partial Differential Equations : Solution in Cartesian coordinate system
Successive Over Relaxation Method
Elliptic Partial Differential Equation in Polar System
Alternating Direction Implicit Method
Treatment of Irregular Boundaries
Methods for Solving tridiagonal System
Hyperbolic Partial Differential Equations
Explicit Method for Solving Hyperbolic PDE
Implicit Method to Hyperbolic PDE
Convergence & Stability
Method of Characteristics
Examples and conclusions
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