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Foundation of Scientific Computing

Foundation of Scientific Computing. Instructor: Prof. Tapan K. Sengupta, Department ofAerospace Engineering, IIT Kanpur. The course covers lessons in Foundation of Scientific Computing, Quantum computing, Wentzel-Kramers-Brillouin Method, Runge-Kutta method, Trapezoidal method, Quasilinear, Laplace equation,wave packets, Pressure fluctuation, linearized shallow water wave equation, 1D convection equation, Upwinding, Numerical amplification factor, Parabolic partial differential equation, Elliptic partial differential equations, Lagrange and hermite interpolations. (from nptel.ac.in)

Lecture 17 - Heat Equation

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Lecture 01 - Introduction

Lecture 02 - Quantum Computing

Lecture 03 - Wentzel-Kramers-Brillouin (WKB) Method

Lecture 04 - Runge-Kutta Method

Lecture 05 - Trapezoidal Method for Step Differential Equation

Lecture 06 - Quasi-linear Partial Differential Equations

Lecture 07 - Laplace Equation

Lecture 08 - Wave Packets

Lecture 09 - Pressure Fluctuation

Lecture 10 - Wave Phenomena: Surface Gravity Waves

Lecture 11 - Linearized Shallow Water Wave Equation

Lecture 12 - 1D Convection Equation

Lecture 13 - Upwinding

Lecture 14 - Numerical Amplification Factor

Lecture 15 - Stiff Differential Equation

Lecture 16 - Spectral Analysis Tool, Numerical Amplification Factor

Lecture 17 - Heat Equation

Lecture 18 - Parabolic Partial Differential Equation

Lecture 19 - Tridiagonal Matrices

Lecture 20 - Error Propagation

Lecture 21 - Elliptic Partial Differential Equations

Lecture 22 - Ordinary Differential Equation

Lecture 23 - Convergence Properties

Lecture 24

Lecture 25 - Alternating Direction Implicit Method, General Elliptic Equation

Lecture 26 - Multigrid Method

Lecture 27 - Multigrid Method (cont.)

Lecture 28 - Spectral Analysis of Explicit and Implicit Schemes

Lecture 29 - Scientific and High Performance Computing

Lecture 30 - Taylor Series Analysis

Lecture 31 - Buffer Domain Technique

Lecture 32 - Aliasing Error

Lecture 33 - Optimized High Accuracy Compact Schemes

Lecture 34 - CCD Scheme

Lecture 35 - Stabilizing Effects of Filters

Lecture 36 - Properties of Filters

Lecture 37 - Scientific Elements of a FEM (Finite Element Method)

Lecture 38 - FEM Basis Functions

Lecture 39 - Elliptic Equation with Linear Basis Function

Lecture 40 - Petrov-Galerkin Method: SUPG Method