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Numerical methods for partial differential equations
Introduction
1. Toolkit Setup
2. Approximations and Taylor expansion
Time integration
3. Euler methods
4. Runge-Kutta methods
Finite differences
6. First-order derivative and slicing
7. Higher order derivatives, functions and matrix formulation
8. Boundary value problems
Partial differential equations
9. The first-order wave equation
10. Matrix and modified wavenumber stability analysis
11. One dimensional heat equation
12. One dimensional heat equation: implicit methods
Iterative methods
13. Iteration methods
14. The conjugate gradient method
15. Boosting Python
Index