Set of programs

• Simple programs: quadratic equation ax^2 + bx + c = 0;
• Fibonacci numbers Fibonacci.cpp
• Single root of f(x)=0: Bisectional method
• Single root of f(x)=0: False position method
• Single root of f(x)=0: Secant method
• Single root of f(x)=0: Newton method
• Single root of f(x)=0: Using 4 methods in one place
• Multiple roots of f(x)=0: Brute force method
• Roots for a system of two nonlinear equations f(x,y)=0, g(x,y)=0: Newton method
• Interpolation: Linear interpolation
• Interpolation: Lagrange n-point interpolation (and example)
• Interpolation: Spline interpolation (and example)
• Integration of f(x) on [a,b]: Trapesoid rule
• Integration of f(x) on [a,b]: Simpson's rule
• Integration of f(x) on [a,b]: Newton-Cotes rule (and example)
• Integration. Three methods: trapezoid, Simpson, Quanc8 (Integral3N)
• Integration. Three methods: Adaptive Simpson, adaptive Gauss-Kronrode, Quanc8 (Integral3A)
• Integration of f(x1,x2) using Newton-Cotes rule twice.
• 1D integration using Monte-Carlo method (code and data)
• nD integration using Monte-Carlo method (code and data)
• Ordinary Differential Equations: first order ODE (Euler, modified Euler, 4th order Runge-Kutta)
• Ordinary Differential Equations: second order ODE (Euler, modified Euler, 4th order Runge-Kutta)
• Ordinary Differential Equations: system of N first order equations (4th order Runge-Kutta)
• Sudoku solver sudoku.cpp with input file (sudoku.dat) and a description (sudoku.txt)

Monte Carlo simulation

• Generating uniform random numbers random1.cpp
• Testing a uniform random generator random2.cpp
• Non-uniform random generator using the rejection method random3.cpp
• Monte Carlo integration 1D by mean value mc_int1.cpp
• Integration of a function using: Trapezoid approximation, Simpson's rule, Monte Carlo method, Newton-Cotes rule integ_4.cpp Attention: you need trapezoid.cpp, simpson.cpp, quanc8.cpp, mc_int1.cpp,
• Or all four methods in one file mc_integral4.cpp,
• Monte Carlo integration nD by mean value mc_int_nd.cpp,

Simple Euler

Runge-Kutta program

Runke Kutta with adaptive step size control

Adaptive step size Runge Kutta ODE solver

Random walk in two dimensions

Acceptance and rejection method with sin(x) distribution

Drell-Yan cross section using two colliding proton beams (make file is here)