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PDE Tutorial

The Finite Difference Method

1. Partial Differential Equations
2. Finite-Difference Approximations
3. Elliptic Partial Differential Equations
4. octave
5. pystencils
6. Introduction to JAX
7. finitediffx
8. kernex
9. py-pde tutorial
10. findiff tutorial
11. Symbolic findiff
12. Solve with findiff
13. AdvectionPer.m
14. DiffusionCrankNic.m
15. Advection pystencils example
16. 1D heat diffusion

The Finite Volume Method

1D advection equation

The Mimetic Finite Difference Method

mole

Simulating Fluid Flows Using Python

17. Introduction to Computational Fluid Dynamics
18. Finite Differences - First Derivative
20. Finite differences in Python
21. Second derivative - 1D heat conduction
22. Introduction to Finite Volume Method
23. CFD Relevant Python Statements | While | For
24. Conduction Visualization Python Script
25. Generalized FVM Formulation
26. 0

Computers, Waves, Simulations

27. First Derivative
28. Second Derivative
29. High-Order Taylor Operators
30. Acoustic Waves 1D I
31. Acoustic Waves 1D II
32. Acoustic Waves 1D - Optimal Operators
33. Acoustic Waves 2D - Heterogeneous case
34. Acoustic Waves 2D - Homogeneous case
35. Advection equation 1D
36. Grid-Staggering Elastic 1D
37. The Pseudo-Spectral Method - Numerical Derivatives based on a Derivative Matrix
38. The Pseudo-Spectral Method - Elastic Wave Equation 1D
39. The Pseudo-Spectral Method - Acoustic Waves in 1D
40. The Pseudo-Spectral Method - Acoustic Waves in 2D
41. The Finite Element Method - Static Elasticity
42. The Finite Element Method - Elastic Wave Equation 1D
43. The Spectral Element Method - Interpolation with Lagrange Polynomials
44. The Spectral Element Method - Numerical Integration - The Gauss-Lobatto-Legendre approach
45. Spectral Element Method - Elastic Wave Equation 1D, Heterogeneous case
46. Spectral Element Method - Elastic Wave Equation 1D - Homogeneous Case

Differential equations and Fourier analysis

47. Fourier series: supplemental material
48. Polynomial interpolation: Lagrange interpolation
51. Numerical solution of ordinary differential equations: High order Runge-Kutta methods
53. Finite difference methods for two-point value problems
57. Numerical integration: Part II
61. Numerical integration: Part IV
64. Introduction to TMA4125
67. A simple epidemic model for Covid 19 and its numerical solution
68. Numerical solution of ordinary differential equations: One step methods
70. Introduction to TMA4125
73. Polynomial interpolation: Newton interpolation
74. Numerical integration
78. Polynomial interpolation: Error theory
80. Numerical solution of ordinary differential equations: Euler’s and Heun’s method
86. Numerical methods for the heat equation

Finite Difference Computing with PDEs

87. Lecture 3

End Matter

Bibliography

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Generalized FVM Formulation

25. Generalized FVM Formulation#

By Carlos Aznarán

Last updated on Oct 05, 2024.

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