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function [u,t] = modifiedeuler(u0,t0,tn,h,f)
//modifiedeuler 1st order method solving ODE
// du/dt = f(u,t), with initial
//conditions u=u0 at t=t0. The
//solution is obtained for t = [t0:h:tn]
//and returned in u
umaxAllowed = 1e+100;
t = [t0:h:tn]; u = zeros(t); n = length(u); u(1) = u0;
for j = 1:n-1
k1=h*f(t(j),u(j));
k2=h*f(t(j)+h/2,u(j)+k1/2);
u(j+1) = u(j) + k2;
if u(j+1) > umaxAllowed then
disp('Euler 1 - WARNING: underflow or overflow');
disp('Solution sought in the following range:');
disp([t0 h tn]);
disp('Solution evaluated in the following range:');
disp([t0 h t(j)]);
n = j; t = t(1,1:n); u = u(1,1:n);
break;
end;
end;
endfunction
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