How can i adapt Euloer backward method

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Solve this by eulor backward method
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
0.0000 1660000.0000
Warning: Ignoring extra legend entries.
10.0000 184259110.0000 20.0000 20452747320.0000 30.0000 2270254903630.0000 40.0000 251998294197040.0000 50.0000 27971810655686552.0000 60.0000 3104870982780921344.0000 70.0000 344640679088681844736.0000 80.0000 38255115378843688370176.0000 90.0000 4246317807051649023213568.0000 100.0000 471341276582733031376158720.0000
then how can i adapt it???
  1 个评论
Torsten
Torsten 2022-8-25
编辑:Torsten 2022-8-25
The code you use isn't Euler backward.
And the formula to compute N''_exist,i is already given (you wrote it in your question). So there is no need to use an Euler backwards integrator from the File Exchange (or whereever you got the code from).

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