04:34
33 4 Week 10 30 4 Meshing and solving the PDE 433
07:21
33 2 Week 10 30 2 Implementing no slip boundaries 720
03:18
33 3 Week 10 30 3 Implementing the boundaries away from wing 317
11:04
30.2 - The variational reduction of the PDE.
12:05
30.4 - Setting up Axb.
11:07
29.3 - Lagrange polynomials.
11:18
29.4 - 2D Lagrange polynomials.
01:37
28.1 - Lecture Overview.
12:17
28.3 - The nonlinear Schrodinger equation.
12:00
30.1 - Building finite element matrices.
10:28
29.2 - Triangularing the computational domain.
14:39
29.1 - The finite element method.
07:51
28.4 - Algorithm for split stepping.
09:44
28.2 - Operator splitting linear and nonlinear terms.
13:54
28.5 - The general splitting method the Trotter product error.
10:09
30.3 - Implementing the finite elements.
10:31
27.2 - Polynomial approximations.
09:47
26.4 - More comparisons.
01:38
25.1 - Lecture Overview.
11:25
27.4 - Building the Chebycheve derivative matrix.
09:16
26.3 - Comparison of coding techniques.
09:29
27.1 - Boundary conditions of spectral methods.
12:11
25.3 - 2D Chebychev differentiation and KRON.
08:47
27.3 - Chebychev points and polynomials.
10:19
27.5 - Implementing the Chebychev matrix.
22:09
25.2 - The Chebychev grid and differentiation.
15:57
25.4 - Implementing the Chebychev function.
11:52
26.2 - The integrating factor for PDEs.
16:25
26.1 - Filtering for removing stiffness.
08:06
22.4 - Modal structures for cosine sine transforms.
12:52
22.3 - Fourier mode expansions.
10:43
24.1 - Programming the Advection Diffusion Equations.
12:01
23.4 - Domain discretization with Chebychev.
17:28
22.5 - Cooley Tukey and the FFT algorithm.
09:28
23.1 - Spectral methods more broadly viewed.
09:53
23.3 - The Chebychev basis functions.
12:21
23.2 - The Chebychev transform.
13:16
24.3 - The time evolution of advection diffusion.
10:47
22.2 - Introduction to spectral methods.
01:42
22.1 - Lecture Overview.
09:24
24.2 - Setting up initial conditions.
16:53
24.4 - Visualization and data processing.
01:20
19.1 - Lecture Overview.
11:00
20.2 - leap frog for the wave equation.
14:31
21.4 - Violating and respecting CFL in the heat equation.
12:28
19.5 - leap frog schemes for one way equation.
15:19
20.4 - Higher order derivatives and numerical stiffness.
11:38
21.2 - Implementing time stepping for the one way wave equation.
13:29
20.1 - Von Neumann analysis for the heat equation.
07:07
19.3 - Stability of forward Euler for one way wave equation.
08:49
19.2 - Von Neumann analysis for stability.
09:01
20.3 - Higher order PDEs and stability.
16:11
19.4 - Von Neumann for alternative schemes for the one way wave equation.
10:02
21.3 - Violating and respecting CFL in the one way wave equation.
12:20
21.1 - Implementing time stepping algorithms and the CFL condition.
10:06
18.5 - Predictor corrector techniques.
13:32
15.2 - Fixing the divide by zero with FFTs.
10:25
16.3 - Computing derivatives with the FFT.
17:51
13.3 - Strict diagonal dominance.
10:34
14.4 - The Fast Poisson Solver.
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