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Question: Need help fitting an equation to data...

Question:Need help fitting an equation to data...

jcumming 4 Maple
May 05 2006
0
I'm trying to fit an equation to some experimental data but I'm not sure how to do it. Could someone here please offer their help? I would really appreciate it. I have three fitting parameters: kT, kU, and A. I will post my worksheet below and I will also attach the part where I begin to try to fit the data in case it doesnt read well when I post it here. > restart > ptotal := 0.0000022 ptotal := 0.0000022 > Ci0 := 1 Ci0 := 1 > d 2 2 > ode := --- pinside(t) = kT (ptotal - pinside(t)) - kU pinside(t) > dt d 2 2 ode := --- pinside(t) = kT (0.0000022 - pinside(t)) - kU pinside(t) dt > ics := pinside(0) = 0 ics := pinside(0) = 0 > dsolve(ode) 1 / pinside(t) = ----------------------- |11 kT 5000000 kT - 5000000 kU / 11 (1/2) 11 (1/2) (1/2) - 11 tanh|------- t (kT kU) + ------- _C1 (kT kU) | (kT kU) | 5000000 5000000 / / > dsolve({ode, ics}) 1 / / pinside(t) = - ----------------- |11 |-kT 5000000 (kT - kU) | | / 11 (1/2) / kT \ (1/2)\ + tanh|------- t (kT kU) + arctanh|------------|| (kT kU) || |5000000 | (1/2)|| || (kT kU) // // > d / kT > ode2 := --- Cinside(t) = ptotal A |------- > dt kT + kU > > 1 / > - ------- |kT > kT - kU > > / / kT \ \ > - tanh|t ptotal sqrt(kT kU) + arctanh|-----------|| sqrt(kT kU)|| Cinside(t) > sqrt(kT kU)// // d / kT 1 / ode2 := --- Cinside(t) = 0.0000022 A |------- - ------- |kT dt |kT + kU kT - kU | / (1/2) / kT \ (1/2)\ - tanh|0.0000022 t (kT kU) + arctanh|------------|| (kT kU) || | | (1/2)|| || (kT kU) // // Cinside(t) > ics2 := Cinside(0) = Ci0 ics2 := Cinside(0) = 1 > dsolve(ode2) / / 11 (1/2) / kT \ / Cinside(t) = |tanh|------- t (kT kU) + arctanh|------------|| - 1|^|- | |5000000 | (1/2)|| | (kT kU) // / A / / 11 (1/2) / kT \ -----------| _C1 |tanh|------- t (kT kU) + arctanh|------------|| + 1|^ 2 (kT - kU)/ | |5000000 | (1/2)|| | (kT kU) // / / A / 11 A kT kU t |- -----------| exp|- -------------------| 2 (kT - kU)/ | / 2 2| 2500000 kT - kU // > dsolve({ics2, ode2}) / / 11 (1/2) / kT \ / Cinside(t) = |tanh|------- t (kT kU) + arctanh|------------|| - 1|^|- | |5000000 | (1/2)|| | (kT kU) // / (1/2) / / A \ | |-------|| | kT - kU/| A |/ kT - kU | -----------| ||-----------------| | 2 (kT - kU)/ || (1/2) | | \(kT kU) + kU/ / (1/2) / / A \ | |-------|| | kT - kU/| |/ (1/2) | ||kT + 2 (kT kU) + kU| | / / 11 (1/2) ||------------------------| | |tanh|------- t (kT kU) || (1/2) | | | |5000000 \ (kT kU) + kU / / / kT \ / A / 11 A kT kU t + arctanh|------------|| + 1|^|- -----------| exp|- -------------------| | (1/2)|| | 2 (kT - kU)/ | / 2 2| (kT kU) // / 2500000 kT - kU // > Cinside := unapply(rhs(%), t) / / 11 (1/2) / kT \ Cinside := t -> |tanh|------- t (kT kU) + arctanh|------------|| - 1|^ | |5000000 | (1/2)|| | (kT kU) // / (1/2) / / A \ | |-------|| | kT - kU/| / A |/ kT - kU | |- -----------| ||-----------------| | 2 (kT - kU)/ || (1/2) | | \(kT kU) + kU/ / (1/2) / / A \ | |-------|| | kT - kU/| |/ (1/2) | ||kT + 2 (kT kU) + kU| | / / 11 (1/2) ||------------------------| | |tanh|------- t (kT kU) || (1/2) | | | |5000000 \ (kT kU) + kU / / / kT \ / A / 11 A kT kU t + arctanh|------------|| + 1|^|- -----------| exp|- -------------------| | (1/2)|| | 2 (kT - kU)/ | / 2 2| (kT kU) // / 2500000 kT - kU // > X := [0, 2, 5, 10, 20, 30, 45, 60, 120, 180, 240] X := [0, 2, 5, 10, 20, 30, 45, 60, 120, 180, 240] > Y := [1, 0.9556, 0.9055, 0.8771, 0.8502, 0.8446, 0.8427, 0.8363, 0.8295, > > 0.8256, 0.8236] Y := [1, 0.9556, 0.9055, 0.8771, 0.8502, 0.8446, 0.8427, 0.8363, 0.8295, 0.8256, 0.8236] > Fit(Cinside(t), X, Y, t, parameternames = [kT, kU, A], > > initialvalues = [0.2, 0.1, 100]) Error, (in Statistics:-Fit) incorrect specification of initial values >
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