Numerical Methods of Ordinary and Partial Differential Equations

Video Lectures

Displaying all 40 video lectures.
I. Ordinary Differential Equations
Lecture 1
Motivation with few Examples
Play Video		 Motivation with few Examples
Lecture 2
Single-Step Methods for IVPs
Play Video		 Single-Step Methods for IVPs
Lecture 3
Analysis of Single-Step Methods
Play Video		 Analysis of Single-Step Methods
Lecture 4
Runge-Kutta Methods for IVPs
Play Video		 Runge-Kutta Methods for IVPs
Lecture 5
Higher Order Methods/Equations
Play Video		 Higher Order Methods/Equations
Lecture 6
Error, Stability, and Convergence of Single-Step Methods
Play Video		 Error, Stability, and Convergence of Single-Step Methods
Lecture 7
Tutorial I
Play Video		 Tutorial I
Lecture 8
Tutorial II
Play Video		 Tutorial II
Lecture 9
Multi-Step Methods (Explicit)
Play Video		 Multi-Step Methods (Explicit)
Lecture 10
Multi-Step Methods (Implicit)
Play Video		 Multi-Step Methods (Implicit)
Lecture 11
Convergence and Stability of Multi-Step Methods
Play Video		 Convergence and Stability of Multi-Step Methods
Lecture 12
General Methods for Absolute Stability
Play Video		 General Methods for Absolute Stability
Lecture 13
Stability Analysis of Multi-Step Method
Play Video		 Stability Analysis of Multi-Step Method
Lecture 14
Predictor-Corrector Methods
Play Video		 Predictor-Corrector Methods
Lecture 15
Some Comments on Multi-Step Methods
Play Video		 Some Comments on Multi-Step Methods
Lecture 16
Finite Difference Methods: Linear BVPs
Play Video		 Finite Difference Methods: Linear BVPs
Lecture 17
Linear/Non-Linear Second Order BVPs
Play Video		 Linear/Non-Linear Second Order BVPs
Lecture 18
BVPS - Derivative Boundary Conditions
Play Video		 BVPS - Derivative Boundary Conditions
Lecture 19
Higher Order BVPs
Play Video		 Higher Order BVPs
Lecture 20
Shooting Method BVPs
Play Video		 Shooting Method BVPs
Lecture 21
Tutorial III
Play Video		 Tutorial III
II. Partial Differential Equations
Lecture 22
Introduction to First Order PDE
Play Video		 Introduction to First Order PDE
Lecture 23
Introduction to Second Order PDE
Play Video		 Introduction to Second Order PDE
Lecture 24
Finite Difference Approximations to Parabolic PDEs
Play Video		 Finite Difference Approximations to Parabolic PDEs
Lecture 25
Implicit Methods for Parabolic PDEs
Play Video		 Implicit Methods for Parabolic PDEs
Lecture 26
Consistency, Stability and Convergence
Play Video		 Consistency, Stability and Convergence
Lecture 27
Other Numerical Methods for Parabolic PDEs
Play Video		 Other Numerical Methods for Parabolic PDEs
Lecture 28
Tutorial IV
Play Video		 Tutorial IV
Lecture 29
Matrix Stability Analysis of Finite Difference Scheme
Play Video		 Matrix Stability Analysis of Finite Difference Scheme
Lecture 30
Fourier Series Stability Analysis of Finite Difference Scheme
Play Video		 Fourier Series Stability Analysis of Finite Difference Scheme
Lecture 31
Finite Difference Approximations to Elliptic PDEs I
Play Video		 Finite Difference Approximations to Elliptic PDEs I
Lecture 32
Finite Difference Approximations to Elliptic PDEs II
Play Video		 Finite Difference Approximations to Elliptic PDEs II
Lecture 33
Finite Difference Approximations to Elliptic PDEs III
Play Video		 Finite Difference Approximations to Elliptic PDEs III
Lecture 34
Finite Difference Approximations to Elliptic PDEs IV
Play Video		 Finite Difference Approximations to Elliptic PDEs IV
Lecture 35
Finite Difference Approximations to Hyperbolic PDEs I
Play Video		 Finite Difference Approximations to Hyperbolic PDEs I
Lecture 36
Finite Difference Approximations to Hyperbolic PDEs II
Play Video		 Finite Difference Approximations to Hyperbolic PDEs II
Lecture 37
Method of characteristics for Hyperbolic PDEs I
Play Video		 Method of characteristics for Hyperbolic PDEs I
Lecture 38
Method of characterisitcs of Hyperbolic PDEs II
Play Video		 Method of characterisitcs of Hyperbolic PDEs II
Lecture 39
Finite Difference Approximations to 1st order Hyperbolic PDEs
Play Video		 Finite Difference Approximations to 1st order Hyperbolic PDEs
Lecture 40
Summary, Appendices, Remarks
Play Video		 Summary, Appendices, Remarks