Numerical methods of Ordinary and Partial Differential Equations


Lecture 1 - Motivation with few Examples


Lecture 2 - Single - Step Methods for IVPs


Lecture 3 - Analysis of Single Step Methods


Lecture 4 - Runge - Kutta Methods for IVPs


Lecture 5 - Higher Order Methods/Equations


Lecture 6 - Error - Stability - Convergence of Single Step Methods


Lecture 7 - Tutorial - I


Lecture 8 - Tutorial - II


Lecture 9 - Multi-Step Methods (Explicit)


Lecture 10 - Multi-Step Methods (Implicit)


Lecture 11 - Convergence and Stability of multi step methods


Lecture 12 - General methods for absolute stability


Lecture 13 - Stability Analysis of Multi Step Methods


Lecture 14 - Predictor - Corrector Methods


Lecture 15 - Some Comments on Multi - Step Methods


Lecture 16 - Finite Difference Methods - Linear BVPs


Lecture 17 - Linear/Non - Linear Second Order BVPs


Lecture 18 - BVPS - Derivative Boundary Conditions


Lecture 19 - Higher Order BVPs


Lecture 20 - Shooting Method BVPs


Lecture 21 - Tutorial - III


Lecture 22 - Introduction to First Order PDE


Lecture 23 - Introduction to Second Order PDE


Lecture 24 - Finite Difference Approximations to Parabolic PDEs


Lecture 25 - Implicit Methods for Parabolic PDEs


Lecture 26 - Consistency, Stability and Convergence


Lecture 27 - Other Numerical Methods for Parabolic PDEs


Lecture 28 - Tutorial - IV


Lecture 29 - Matrix Stability Analysis of Finite Difference Scheme


Lecture 30 - Fourier Series Stability Analysis of Finite Difference Scheme


Lecture 31 - Finite Difference Approximations to Elliptic PDEs - I


Lecture 32 - Finite Difference Approximations to Elliptic PDEs - II


Lecture 33 - Finite Difference Approximations to Elliptic PDEs - III


Lecture 34 - Finite Difference Approximations to Elliptic PDEs - IV


Lecture 35 - Finite Difference Approximations to Hyperbolic PDEs - I


Lecture 36 - Finite Difference Approximations to Hyperbolic PDEs - II


Lecture 37 - Method of characteristics for Hyperbolic PDEs - I


Lecture 38 - Method of characterisitcs for Hyperbolic PDEs - II


Lecture 39 - Finite Difference Approximations to 1st order Hyperbolic PDEs


Lecture 40 - Summary, Appendices, Remarks