Numerical methods

Numerical methods

Source: Wikipedia

Table of contents:

1. Introduction to Modelling

2. Interpolation and curve fitting

   • Interpolation

   • Curve fitting

   • Extrapolation

3. Numerical differentiation

   • Forward difference method (FDM)

   • Central difference method (CDM)

   • Second derivative

4. Solving differential equations

   • Solving or timestepping an ODE

   • Forward Euler scheme

   • Heun’s method

   • Runge-Kutta method

   • Successive over-relaxation method

   • FTCS scheme

   • BTCS scheme

5. Numerical integration

   • Midpoint rule (rectangle method)

   • Trapezoid rule

   • Simpson’s rule

   • Composite Simpson’s rule

   • Weddle’s rule

6. Roots of equations

   • Picard’s method of successive approximations (or fixed point iteration)

   • Root bracketing

   • Bisection method

   • Newton method

   • (Quasi-) Newton with approximate derivative

   • Secant method

7. Numerical linear algebra

   • Gaussian elimination

   • Gauss-Jordan elimination

   • LU decomposition

   • Ill-conditioning and roundoff errors

   • Iterative methods to solve a matrix

   • Sparse matrices

References

• Material used in this notebook was based on lecture content of Numerical Methods 1 (by Prof. Matthew Piggott) and Numerical Methods 2 (by Prof. Stephen Neethling) at Earth Science and Engineering Department at Imperial College London