Richard Clift PROGRAMS 
    
        
    Gardner equation Numerical: Solves the Gardner equation using method of lines
    gkdv.m function file for numerical Gardner equation
  
    Gardner Analytical: Uses the analyitcal solution of the Whitham modulation equations
    with a step initial condition.
    
    Hydraulic solution: Solves analytically the Steady non-dispersive Gardner equation with forcing
   
    ab continuation: This program use numerical continuation to illustrate the computation of stationary solutions, Hopf bifurcations and periodic
solutions, and the computation loci of folds and Hopf bifurcation points.
It plots the eigenvalues of the system so the point of the Hopf bifurcation can be illustrated.
local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex
conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane
Monte Carlo approximation of Pi: An approximation of pi can be found using random numbers. This done by taking the ratio of the areas of a circle enclosed in a square of radius 1 which gives pi. Now produce a random point that is within the square. The ratio of the number of points in the square over the number of points in the circle is pi. The program is a function file for MATLAB and takes in the number of points use want to use. The value 1000000 gives a good result for pi. Below is an animation of what is happening graphically. 
    
        
    Lax Pair: This is a small file for Mathematica that produces the lax pair calculations
    for given matrices U and V
    
    
        
    Poincare Section: This program solves numerically a nonlinear ode and takes poincare sections of the periodic orbit
   and the eigenvalues are then found to find the Floquet multipliers.
   In order to get Floquet Multipliers, you need to integrate the Variational
Equation along with the original ODE.
Runga kutta C++: This program solves numerically a simple ode using a 4th order runge kutta scheme in C++ Sieve C++: This program gives the first 1000 primes using the algorithm Sieve of Eratosthenes