Roots of nonlinear equations

• Five methods for finding roots Root5.m (bisectional, false position, secant, brute force and using matlab)

Integration

• Automatic adaptive integration - Newton-Cotes quadrature Quanc8.m
• Trapezoid, Simpson and Gauss quadrature - effect of number of intervals IntegralN.m

Ordinary Differential Equations (Initial Value Problem)

• First-order ODE (choose a method) ODE1.m
• First-order ODE (three methods) ODE1_3.m
• First-order ODE (RKF45 method) Ode1Rkf45.m
• Second-order ODE (RKF45 method) Ode2Rkf45.m
• Pendulum d2x/dt2 = (-1.0*omega0^2)*sin(x) - alpha*(dx/dt) + force*cos(omega*t) Pendulum2022.m
• System of n first-order ODE equations ODEn.m

Ordinary Differential Equations (Boundary Value Problem)

• Method: equilibrium with Dirichlet boundary conditions ODE_FDM1.m
• Method: equilibrium with various boundary conditions ODE_FDM3.m
• Method: Shooting with Dirichlet boundary conditions ODE_Shoot1.m
• Solving Schrodinger equation using the shooting method SchrodingerSM.m
• Solving Schrodinger equation using the equilibrium (FDM) method SchrodingerFDM3.m

Partial Differential Equations

• Poisson equation with Dirichlet boudary conditions PDE_EPoisson.m
• Heat equation with Dirichlet boudary conditions (2 methods: FTCS and BTCS) PDE_PHeat.m

Monte-Carlo Method

• Uniform random number generator (testimg) Rng1Uniform.m
• Non-uniform RNG (the rejection method) Rng2Reject.m
• Non-uniform RNG (three method: rejection, transform, Metropolis) Rng3Methods.m
• Monte-Carlo integration by mean value: IntegralMC1.m
• Monte-Carlo integration without and with sampling: IntegralMC3.m
• Random walk: simple 2D random walk: rwalk01.m
• Random walk: 2D random walk in a city: rwalk02.m
• Random walk: 2D random walk in a city: rwalk02.m
• Random walk: 2D random walk in a city with a trap: rwalk03.m
• Random walk: 2D sefl-avoiding random walk (polymer growing): Rwalk2.m