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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