How can I change this code to euler backward method? (implicit method)

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민석 최
민석 최 2022-6-7
编辑： Torsten 2022-6-7
f = @(t,y) -100000*y + 99999*exp(-t);
t0 = 0; y0 =0;
h = 0.01; tn = 2;
n = (tn-t0)/h;
t(1)=t0; y(1)=y0;
for i=1:n
t(i+1) = t(i) + h;
y(i+1) = y(i) + (f(t(i),y(i))*h);
end
plot(t,y)

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Torsten
Torsten 2022-6-7
编辑：Torsten 2022-6-7
Ran in:
f = @(t,y) -100000*y + 99999*exp(-t);
t0 = 0; y0 =0;
h = 0.01; tn = 2;
n = (tn-t0)/h;
t(1)=t0; y(1)=y0;
for i=1:n
t(i+1) = t(i) + h;
fun = @(x) x - y(i) - h*f(t(i+1),x);
y(i+1) = fzero(fun,y(i));
end
plot(t,y)
hold on
exact = @(t) exp(-t)-exp(-100000*t);
plot(t,exact(t))

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