Topic 14.6: Stiff Differential Equations (Maple)

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Given the IVP y⁽¹⁾(t = -21 y(t) + e^-t y(0) = 0, to approximate y(t) on [0, 2] with h = 0.1, we can do:

N := 20:
t[0] := 0:
h := 0.1:
f := (t, y) -> -21*y + exp(-t):
for i from 1 to N do
    t[i] := t[0] + i*h;
end do:
y[0] := 0:
for i from 1 to N do
    y[i] := fsolve( upsilon - y[i - 1] = h*f( t[i], upsilon ) = 0 );
end do:
plots[pointplot]( [seq( [t[i], y[i]], i = 0..N )] );

Here we let Maple's fsolve routine fine the root of our equation.