Mathematics - Numerical methods of Ordinary and Partial (English)

   Sunday, April 06, 2025   

Starting a new Lecture Notes Series on Mathematics - Numerical methods of Ordinary and Partial

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Lecture 1: Mod-01 Lec-01 Motivation with few Examples

Lecture 2: Mod-02 Lec-02 Single - Step Methods for IVPs

Lecture 3: Mod-03 Lec-03 Analysis of Single Step Methods

Lecture 4: Mod-04 Lec-04 Runge - Kutta Methods for IVPs

Lecture 5: Mod-05 Lec-05 Higher Order Methods/Equations

Lecture 6: Mod-06 Lec-06 Error - Stability - Convergence of Single Step Methods

Lecture 7: Mod-07 Lec-07 Tutorial - I

Lecture 8: Mod-08 Lec-08 Tutorial - II

Lecture 9: Mod-09 Lec-09 Multi-Step Methods (Explicit)

Lecture 10: Mod-10 Lec-10 Multi-Step Methods (Implicit)

Lecture 11: Mod-11 Lec-11 Convergence and Stability of multi step methods

Lecture 12: Mod-12 Lec-12 General methods for absolute stability

Lecture 13: Mod-13 Lec-13 Stability Analysis of Multi Step Method

Lecture 14: Mod-14 Lec-14 Predictor - Corrector Methods

Lecture 15: Mod-15 Lec 15 Some Comments on Multi - Step Methods

Lecture 16: Mod-16 Lec-16 Finite Difference Methods - Linear BVPs

Lecture 17: Mod-17 Lec 17 Linear/Non - Linear Second Order BVPs

Lecture 18: Mod-18 Lec-18 BVPS - Derivative Boundary Conditions

Lecture 19: Mod-19 Lec-19 Higher Order BVPs

Lecture 20: Mod-20 Lec-20 Shooting Method BVPs

Lecture 21: Mod-21 Lec-21 Tutorial - III

Lecture 22: Mod-22 Lec-22 Introduction to First Order PDE

Lecture 23: Mod-23 Lec-23 Introduction to Second Order PDE

Lecture 24: Mod-24 Lec-24 Finite Difference Approximations to Parabolic PDEs

Lecture 25: Mod-25 Lec-25 Implicit Methods for Parabolic PDEs

Lecture 26: Mod-26 Lec-26 Consistency, Stability and Convergence

Lecture 27: Mod-27 Lec-27 Other Numerical Methods for Parabolic PDEs

Lecture 28: Mod-28 Lec-28 Tutorial - IV

Lecture 29: Mod-29 Lec-29 Matrix Stability Analysis of Finite Difference Scheme

Lecture 30: Mod-30 Lec-30 Fourier Series Stability Analysis of Finite Difference Scheme

Lecture 31: Mod-31 Lec-31 Finite Difference Approximations to Elliptic PDEs- I

Lecture 32: Mod-32 Lec-32 Finite Difference Approximations to Elliptic PDEs - II

Lecture 33: Mod-33 Lec-33 Finite Difference Approximations to Elliptic PDEs - III

Lecture 34: Mod-34 Lec-34 Finite Difference Approximations to Elliptic PDEs - IV

Lecture 35: Mod-35 Lec-35 Finite Difference Approximations to Hyperbolic PDEs - I

Lecture 36: Mod-36 Lec-36 Finite Difference Approximations to Hyperbolic PDEs - II

Lecture 37: Mod-37 Lec-37 Method of characteristics for Hyperbolic PDEs - I

Lecture 38: Mod-38 Lec-38 Method of characterisitcs of Hyperbolic PDEs - II

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

Lecture 40: Mod-40 Lec-40 Summary, Appendices, Remarks