UsefulLinks
Physics
Applied and Interdisciplinary Physics
Computational Physics
1. Introduction to Computational Physics
2. Mathematical Foundations
3. Programming Fundamentals
4. Computer Arithmetic and Error Analysis
5. Root Finding Methods
6. Numerical Differentiation
7. Numerical Integration
8. Linear Systems
9. Eigenvalue Problems
10. Ordinary Differential Equations
11. Partial Differential Equations
12. Monte Carlo Methods
13. Molecular Dynamics
14. Data Analysis and Visualization
15. Applications in Classical Mechanics
16. Applications in Electromagnetism
17. Applications in Quantum Mechanics
18. Applications in Statistical Mechanics
19. Applications in Fluid Dynamics
20. High-Performance Computing
11.
Partial Differential Equations
11.1.
Classification of PDEs
11.1.1.
Elliptic PDEs
11.1.2.
Parabolic PDEs
11.1.3.
Hyperbolic PDEs
11.2.
Finite Difference Methods
11.2.1.
Spatial Discretization
11.2.2.
Temporal Discretization
11.2.3.
Boundary Conditions
11.3.
Elliptic Equations
11.3.1.
Laplace Equation
11.3.2.
Poisson Equation
11.3.3.
Iterative Solution Methods
11.3.4.
Multigrid Methods
11.4.
Parabolic Equations
11.4.1.
Heat Equation
11.4.2.
Diffusion Equation
11.4.3.
Explicit Methods
11.4.4.
Implicit Methods
11.4.5.
Crank-Nicolson Method
11.5.
Hyperbolic Equations
11.5.1.
Wave Equation
11.5.2.
Advection Equation
11.5.3.
Upwind Schemes
11.5.4.
Lax Methods
11.5.5.
CFL Condition
11.6.
Finite Element Methods
11.6.1.
Weak Formulation
11.6.2.
Basis Functions
11.6.3.
Mesh Generation
11.6.4.
Assembly Process
11.7.
Spectral Methods
11.7.1.
Fourier Spectral Methods
11.7.2.
Chebyshev Spectral Methods
11.7.3.
Pseudospectral Methods
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10. Ordinary Differential Equations
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12. Monte Carlo Methods