Help with user defined function to solve an ODE with modified euler predict-corrector method

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Zi Jing
Zi Jing 2014-12-1
Hi, I need to find the [t,y] values for the ODE dy/dt=t^2-3*y/t in the range of t=[1-2.2] with IC: [t1,y1]=[1,1]
for far my code is:
clear all; close all; clc;
dy_dt=@(t, y) t.^2-3*y/t;
t(1)=1;
y(1)=1;
yfinal(1)=1;
h=0.1;
no_points=(2.2-1)/h +1;
%% Loop from 2nd point to last point and apply Euler's steps
for i=2:no_points
t(i)=t(i-1)+h; % Calculate x value of the current point
slope(i-1)=dy_dt(t(i-1),y(i-1)); % Calculate slope at previous point
y(i)=y(i-1)+slope(i-1)*h; % Calculate y value of the current point
j=1;
y(j)=y(i);
for j=2:100 %attempt at modified method, with predictor-corrector
slopemod(j-1)=slope(i-1)+dy_dt(t(i),y(i));
ymodeu(j)=y(i-1)+slopemod(j-1)*h*0.5;
Tol(j)=abs((ymodeu(j)-y(j-1))/y(j-1));
if Tol(j) < 0.0005
yfinal(i)=ymodeu(j) % Save the Solution
t(i)
break;
else
y(i)=ymodeu(j);
end
end
end
I feel like the logic follows but it just doesn't work... please help

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