Hugo-Diaz-N

function [mu,m]=SmoothSpline(X,f,p)

% [mu,m]=SmoothSpline(X,f,p)
% 
% This code compute the parameter of "the smoothing natural spline" 
% for the data  (x_i,f_i) with weights {p_i} i.e. the solution of
%
%     \min\Biggl\{ \sum_{i=0}^N p_i\left(\hat{f}(x_i)-f_i \right)^2
%                  +\int_{a}^{b} \bigl|\hat{f}''(x)\bigr|^2dx \Biggr\}
% Input:  

Hugo-Diaz-N

function p=ChebyshevInterp(f,n,xx)
n = n-1;                            % Number intervals
Xn = cos((pi/(n+1))*(0.5+(0:n)));   % Chebyshev Nodes
f_X = f(Xn);                        % f at Chebyshev nodes,                 
omega = BaryWeigths(Xn);            % Barycentric Weigths.
p = zeros(1,length(xx));            % Setting interpolant
is = ismember(xx,Xn);               % Position of a member of Xn at xx.
p(is) = f(xx(is));                  % p(x_k) =f(x_k). 
xx = setdiff(xx,Xn);                % xx \setminus Xn.
A = repmat(Xn',1,100);

Hugo-Diaz-N

function [flag,xk1] = RationalCode(x0,f,df,d2f,TOL,MaxIt)

%[flag,xk] = RationalCode(x0,f,df,d2f,TOL,MaxIt)
% 
% This code approximate a root of f using a rational fuction approx.
% Input:  
%          x0  := initial value.
%           f  := function whose roots will be approximated.
%          df  := derivative of f.
%         d2f  := second derivative of f.

Hugo-Diaz-N

% Problem: find u s.t.
% \frac{d}{dt}{\bf u}(t)+\alpha {\bf u}(t)\times \frac{d}{dt}{\bf u}(t)&={\bf u}(t)\times {\bf F}(t)
% initial position u_0=0.5*\sqrt(2)(0 1 1)^t

F=[0 0 10]'; % constant case
u0=0.5*sqrt(2)*[0 1 1]';
a=0.1; % alpha in the PDE
b=(1/(1+a*a*norm(u0,2)^2));
f=@(t,u) b*(cross(u,F)-a*(F'*u)*u+a*norm(u)^2*F);
[t,w]=ode23s(f,[0,10],u0);

Hugo-Diaz-N

%---------------- Setting Problem --------------------%
x0  =  0.994;                % x(0)  Initial position
y0  =  0.0;                  % y(0)  Initial position
dx0 =  0.0;                  % x'(0) Initial velocity
dy0 = -2.031732629557;       % y'(0) Initial velocity
%-----------------------------------------------------%
%---------------- Setting Model ----------------------%
mu1 = 0.012277471;          % Moon mass,  M_m/(M_e+M_m) 
mu2 = 1-mu1;                % Earth mass, M_e/(M_e+M_m) 
%-----------------------------------------------------%