Locating roots of equation
1) Bisection method
2) Newton method
3) Secant method
Ordinary differential equation
1) Taylor series method
2) Rung-Kutta method
3) Secant method
1) Bisection method
2) Newton method
3) Secant method
Ordinary differential equation
1) Taylor series method
2) Rung-Kutta method
3) Secant method
Numerical integration
1) Lower and upper sums
2) Trapezoid rule
3) Romberg algorithm
4) Simpson & ASR
5) Gaussian quadrature formulas
Monte carlo method and simulation
1) Random numbers & generators
2) Transformation method
3) Area & Volume estimation br MC
4) Importance sampling
5) 2D Ising
1) Lower and upper sums
2) Trapezoid rule
3) Romberg algorithm
4) Simpson & ASR
5) Gaussian quadrature formulas
Monte carlo method and simulation
1) Random numbers & generators
2) Transformation method
3) Area & Volume estimation br MC
4) Importance sampling
5) 2D Ising
System of linear equations
1) Naive Gaussian elimination
2) Gaussian elimination with SPP
3) Tridiagonal and banded systems
4) Matrix factorization
5) Eigenvalues and eigenvectors
Smoothing of data & LSM
1) Errors and uncertainties
2) Linear & nonlinear LSM
3) Data Fitting
4) Chi square test
1) Naive Gaussian elimination
2) Gaussian elimination with SPP
3) Tridiagonal and banded systems
4) Matrix factorization
5) Eigenvalues and eigenvectors
Smoothing of data & LSM
1) Errors and uncertainties
2) Linear & nonlinear LSM
3) Data Fitting
4) Chi square test
Here we need a programming language and simulation software. We recommend FORTRAN as programming language and LAMMPS as simulation software. FORTRAN is fast (in offline processing) and stands for “formula translation” and easy to learn for physicists. C++ and C are fast too but python is much slower with amazing features. So it’s depends on you to choose carefully.
To install & learn about FORTRAN and python you could see my skill page :
Fortran link : https://bakhshiali.com/en/skills/fortran/
Python link : https://bakhshiali.com/en/skills/python/
Locating roots of equation
1) Bisection method
2) Newton method
3) Secant method