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function [t,x]=pred_corr(field,t0,T,x0,h)
%PRED_CORR Implements the PECECE Predictor/Corrector algorithm using
% Adams-Bashfort 2 (Predictor) and Adams-Moulton 2 (Corrector)
%
% Parameters:
% field -- Right hand side function of ODE system: x'=f(t,x)
% t0 -- Initial time
% T -- End time (T > t0)
% x0 -- Initial value
% h -- Size of time step (h <= T-t0)
%
% Outputs:
% t -- [t0; t-0+h, t0+2*h; ...; t0+i*h; ...]
% x -- Column vector containing numerical solution at each time step
q = 1;
n = ceil((T-t0)/h);
t = t0+h*(0:n).';
x = ones(n+1,length(x0));
[t(1:(q+1)), x(1:(q+1),:)] = rk_classical(field, t0, t0+q*h, x0, h);
f1 = feval(field, t(q), x(q,:).');
f0 = feval(field, t(q+1), x(q+1,:).');
for i=(q+1):n
x0 = x(i,:).'+h*(3*f0-f1)/2; % P - ab2
f_new = feval(field, t(i,:)+h, x0); % E
x0 = x(i,:).' + h*(5*f_new+8*f0-f1)/12; % C - am2
f_new = feval(field, t(i,:)+h, x0); % E
x0 = x(i,:).' + h*(5*f_new+8*f0-f1)/12; % C - am2
f_new = feval(field, t(i,:)+h, x0); % E
x(i+1,:) = x0;
f1 = f0;
f0=f_new;
end
