scientific-computing-algorithms

This repo stores my revision and implementations of numerical methods in mathematics (written in Python), including:

• Differentiation
  • Forward difference
  • Backward difference
  • Central difference
  • Source file: Python
• Root finding
  • Bisection method
  • Newton's method
  • Secant method
  • Source file: Python
• Integration
  • Midpoint rule
  • Trapezoidal rule
  • Simpson's rule
  • Adaptive integration, e.g. quad.m in MATLAB
  • Source file: Python
• Differential equations
  • Euler method
  • Modified Euler method
  • Midpoint method
  • Second-order Runge-Kutta methods
  • Fourth-order Runge-Kutta methods
  • Source file: Python
• And More!

Targets

To finish this repo, I will implement the numerical methods suggested in the reference, and also to make notes on different topics. Apart from the references, I would also like to include some topics that I have hands-on expereience during my research studies. For example:

• Mathematical optimization
• Kalman filtering
• Structural dynamics
• Bayesian model updating

References

Lecture Notes on Scientific Computing (Harvey Mudd College, Math 164). Prof. Jeffrey R. CHASNOV. HKUST.

Mathematical Python. Dr. Patrick Walls. UBC.