Blatt8 Num2

function Aufgabe8_24()
  h=0.1;
  t=[0:0.1:0.5];
  y=zeros(6,1);
  y(1)=1;
  k1 = f(t(1), y(1));
    k2 = f(t(1) + h/2, y(1) + h/2*k1);

    y(2) = y(1) + h*k2;

  k1 = f(t(2), y(2));
    k2 = f(t(2) + h/2, y(2) + h/2*k1);

    y(3) = y(2) + h*k2;


  y0=y;

  for i=4:6
    y0(i)=m1(y(i-1),y(i-2),y(i-3),@(t, z) 2*t*z^2*exp(-t^2),t(i-3),h);

    y(i)=m2(y(i-1),y0(i),y(i-1),y(i-2), @(t, z)2*t*z^2*exp(-t^2),t(i-3),h);

  endfor

  y0
  y


endfunction




function r= m1(a,b,c,f,t,h)
  r=a+h*(23/12*f(t+2*h,a)-4/3*f(t+h,b)+5/12*f(t,c));

endfunction

function r=m2(a,b,c,d,f,t,h)
  r=a+h*(5/12*f(t+3*h,b)+2/3*f(t+2*h,c)-1/12*f(t+h,d));

endfunction

function r= f(t,z)
  r=2*t*z^2*exp(-t^2);
endfunction