Numerical Solution of Ordinary & Partial Differential Equations

Media Storage Type : DVD-ROM

NPTEL Course Name : Numerical Solution of Ordinary and Partial Differential Equations

NPTEL Subject Matter Expert : Dr. Sunita Gakkhar

NPTEL Co-ordinating Institute : IIT Roorkee

NPTEL Lecture Count : 40

Lecture Titles:

Lecture 1 - Numerical solution of first order ordinary differential equations
Lecture 2 - Numerical Methods: Euler method
Lecture 3 - Modified Euler Method
Lecture 4 - Runge Kutta Method
Lecture 5 - Fourth Order Runge Kutta Methods
Lecture 6 - Higher order Runge Kutta Methods
Lecture 7 - Multi Step Methods Predictor corrector Methods
Lecture 8 - Multi Step Methods Predictor corrector Methods (Continued...)
Lecture 9 - Multi Step Methods Adams Bashforth method
Lecture 10 - Multi Step Methods Adams Moulton method
Lecture 11 - Systems of Differential Equations
Lecture 12 - Higher Order Equations
Lecture 13 - Stiff Differential equations
Lecture 14 - Finite Difference Methods: Dirichlet type boundary condition
Lecture 15 - Finite Difference Methods: Mixed boundary condition
Lecture 16 - Shooting Method
Lecture 17 - Shooting Method contdï¾…
Lecture 18 - Solution by Finite Difference Methods
Lecture 19 - Shooting Methods
Lecture 20 - Shooting Methods (Continued...)
Lecture 21 - Introduction of PDE, Classification and Various type of conditions
Lecture 22 - Finite Difference representation of various Derivatives
Lecture 23 - Parabolic Partial Differential Equations : One dimensional equation : Explicit method.
Lecture 24 - Crank Nicolson method and Fully Implicit method
Lecture 25 - Three Time Level Schemes
Lecture 26 - Extension to 2d Parabolic Partial Differential Equations
Lecture 27 - Compatibility and Stability of 1d Parabolic PDE
Lecture 28 - Stability of one-dimensional Parabolic PDE
Lecture 29 - Convergence of one?dimensional Parabolic PDE
Lecture 30 - Elliptic Partial Differential Equations : Solution in Cartesian coordinate system
Lecture 31 - Successive Over Relaxation Method
Lecture 32 - Elliptic Partial Differential Equation in Polar System
Lecture 33 - Alternating Direction Implicit Method
Lecture 34 - Treatment of Irregular Boundaries
Lecture 35 - Methods for Solving tridiagonal System
Lecture 36 - Explicit Method for Solving Hyperbolic PDE
Lecture 37 - Implicit Method to Hyperbolic PDE
Lecture 38 - Convergence and Stability
Lecture 39 - Method of Characteristics
Lecture 40 - Examples and conclusions