How can i adapt Euloer backward method
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![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1107280/image.png)
Solve this by eulor backward method
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1107285/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1107290/image.png)
then I write BW code in matlab simply
% dy/dt=y-t^2+1 ; 0<=t<=2 ; y(0)=0.5;
clc,clear;close all;
f = @(t,y) (y-t^2+1);
a = 0; %input('initial ponit, a: ');
b = 100; %input('end point, b: ');
n = 10; %input('intervals, n: ');
alpha = 166*10^(4); %input('initial condition, alpha: ');
h = (b-a)/n;
t=[a zeros(1,n)];
y=[alpha zeros(1,n)];
for i = 1:n+1
t(i+1)=t(i)+h;
yprime=y(i)+h*f(t(i),y(i)); %slope
y(i+1)=y(i)+h*f(t(i+1),yprime);
delta=y(i+1)-yprime;
fprintf('%.4f %.4f\n', t(i), y(i));
figure(1)
plot(t(i),y(i),'r*');
grid on;
plot(t(i),delta,'g*',t(i),yprime,'b*');
xlabel('t values'); ylabel('y values');
hold on;
legend('delta','yprime','BW')
end
then how can i adapt it???
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