Clear["Global'*"];
nut = 46; khi = 16; ro2 = 3400; kmrs = 4; kisu = 1.5; kmp = .5; kres \
= 25;
kccc1 = 38; k23 = 16; kvp = .04; kc = 21; nc = 5; km1 = 24; nm1 = 3;
km2 = 45; nm2 = 4; kv1 = 17; nv1 = 6; kv2 = 200; nv2 = 4; k32 = 18; \
n32 = 9; a = .5;
odec = -(a c[t]) - (
kccc1 c[t] (1 - 1/((c[t]/kv1)^nv1 + 1)))/((f3[t]/kv2)^nv2 + 1) - (
kmrs c[t])/((fm[t]/km2)^nm2 + 1) + (khi nut)/((c[t]/kc)^nc + 1);
odefm = -(a fm[t]) + (kmrs c[t])/((fm[t]/km2)^nm2 + 1) - kisu fm[t] -
kmp fm[t] o2[t];
odefs = kisu fm[t] - a fs[t];
odemp = kmp fm[t] o2[t] - a mp[t];
odeo2 = -(kmp fm[t] o2[t]) - kres fs[t] o2[t] +
ro2/((o2[t]/245)^9 + 1);
odef2 = -(a f2[t]) - k23 f2[t] (1 - 1/((c[t]/k32)^n32 + 1)) + (
kccc1 c[t] (1 - 1/((c[t]/kv1)^nv1 + 1)))/((f3[t]/kv2)^nv2 + 1);
odef3 = -(a f3[t]) + k23 f2[t] (1 - 1/((c[t]/k32)^n32 + 1)) -
kvp f3[t];
odevp = kvp f3[t] - a vp[t];
vars = {c[t], f2[t], f3[t], fm[t], fs[t], mp[t], o2[t], vp[t]};
solution =
NDSolve[{Derivative[1][c][t] == odec, Derivative[1][f2][t] == odef2,
Derivative[1][f3][t] == odef3, Derivative[1][fm][t] == odefm,
Derivative[1][fs][t] == odefs, Derivative[1][mp][t] == odemp,
Derivative[1][o2][t] == odeo2, Derivative[1][vp][t] == odevp,
c[0] == 30, f2[0] == 100, f3[0] == 100, fm[0] == 50, fs[0] == 50,
mp[0] == 0, o2[0] == 100, vp[0] == 100}, vars, {t, 0, 31}];
vars
vars /. solution /. t -> 500
I am curious about the extrapolation "error" that is produced when I go beyond the range of the interpolating function window. When I stay within the interpolating function, (expanding the window from {t, 0, 31} to say 1000) and go out to the limit of the window I produce the same values at the plateau around t=30. Are the extrapolated values I am getting from the interpolation function solutions viable? Is there a way to evaluate the error on these values?
