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What went wrong with this NDSolve command usage?

Dear All,

I got error message when trying to solve an equation by using NDSolve command. This is my equation:

  sol = NDSolve[{q'[t] == (a q[t]^b newefrainfunc[t] - q[t]) + (a q[t]^b sigmaer1[t]), q[1] == q0}, q, {t, 1, 456}]

where: a, b, and q0 are given constant values; newefrainfunc[t_] = newefrain, where newefrain=Table[rainfun[t]ff, {t, 1, 456}]; sigmaer1[t_]=newefrain - newefrain1, where newefrain1=Table[rainfun[t]ff1, {t, 1, 456}]

But when I run the script, I got an error message as follows:

NDSolve::ndfdmc: Computed derivatives do not have dimensionality consistent with the initial conditions. >>

NDSolve[{Derivative[1][q][t] == {0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 11.3171 q[t]^0.006286 - q[t], 
    3.77239 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 113.219 q[t]^0.006286 - q[t], 
    151.199 q[t]^0.006286 - q[t], 18.9052 q[t]^0.006286 - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 11.3451 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 343.199 q[t]^0.006286 - q[t], 
    84.137 q[t]^0.006286 - q[t], 0. - q[t], 
    3.82495 q[t]^0.006286 - q[t], 65.1857 q[t]^0.006286 - q[t], 
    0. - q[t], 7.67124 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 57.671 q[t]^0.006286 - q[t], 
    50.0905 q[t]^0.006286 - q[t], 116.225 q[t]^0.006286 - q[t], 
    58.2834 q[t]^0.006286 - q[t], 42.8373 q[t]^0.006286 - q[t], 
    42.9368 q[t]^0.006286 - q[t], 39.1184 q[t]^0.006286 - q[t], 
    138.025 q[t]^0.006286 - q[t], 47.4618 q[t]^0.006286 - q[t], 
    0. - q[t], 7.91423 q[t]^0.006286 - q[t], 0. - q[t], 
    23.7784 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 31.7692 q[t]^0.006286 - q[t], 
    75.8284 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    19.9816 q[t]^0.006286 - q[t], 108.711 q[t]^0.006286 - q[t], 
    646.845 q[t]^0.006286 - q[t], 873.149 q[t]^0.006286 - q[t], 
    819.296 q[t]^0.006286 - q[t], 408.903 q[t]^0.006286 - q[t], 
    148.225 q[t]^0.006286 - q[t], 61.6501 q[t]^0.006286 - q[t], 
    51.5953 q[t]^0.006286 - q[t], 10.3279 q[t]^0.006286 - q[t], 
    20.6911 q[t]^0.006286 - q[t], 10.3544 q[t]^0.006286 - q[t], 
    31.143 q[t]^0.006286 - q[t], 0. - q[t], 
    20.7976 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 5.20161 q[t]^0.006286 - q[t], 
    5.20383 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    26.0748 q[t]^0.006286 - q[t], 26.1305 q[t]^0.006286 - q[t], 
    10.4611 q[t]^0.006286 - q[t], 36.7236 q[t]^0.006286 - q[t], 
    36.8334 q[t]^0.006286 - q[t], 31.6523 q[t]^0.006286 - q[t], 
    5.27764 q[t]^0.006286 - q[t], 15.8532 q[t]^0.006286 - q[t], 
    10.5778 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 15.887 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 
    10.6003 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 10.6094 q[t]^0.006286 - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    15.9344 q[t]^0.006286 - q[t], 53.341 q[t]^0.006286 - q[t], 
    69.7271 q[t]^0.006286 - q[t], 32.2638 q[t]^0.006286 - q[t], 
    5.37957 q[t]^0.006286 - q[t], 0. - q[t], 
    21.5548 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 280.801 q[t]^0.006286 - q[t], 
    55.2904 q[t]^0.006286 - q[t], 0. - q[t], 
    270.758 q[t]^0.006286 - q[t], 412.347 q[t]^0.006286 - q[t], 
    34.9313 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 11.6532 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    11.6627 q[t]^0.006286 - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 5.83369 q[t]^0.006286 - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 11.6768 q[t]^0.006286 - q[t], 
    17.5365 q[t]^0.006286 - q[t], 153.584 q[t]^0.006286 - q[t], 
    59.3078 q[t]^0.006286 - q[t], 29.7132 q[t]^0.006286 - q[t], 
    0. - q[t], 5.94502 q[t]^0.006286 - q[t], 
    47.712 q[t]^0.006286 - q[t], 29.8794 q[t]^0.006286 - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 0. - q[t], 
    0. - q[t]}, q[1] == 1}, q, {t, 1, 456}]

So may I know what possibly went wrong with my equation? Thanks in advance for your help!

Best Regards, Intan
POSTED BY: INTAN SUPRABA
2 Replies
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Hi,

The problem is that you trying to use lists as functions. Make functions from your list with Interpolation[]. Here is a simple example:

Plot[#, {s, 0, 10.}] &@ NDSolveValue[{q'[s] == Sin[s] q[s], q[0] == 1}, q[s], {s, 0, 10.}]
sin = Interpolation[Table[{s, Sin[s]}, {s, 0., 10., 0.1}]];
Plot[#, {s, 0, 10.}] &@  NDSolveValue[{q'[s] == sin[s] q[s], q[0] == 1}, q[s], {s, 0, 10.}]

I.M.
POSTED BY: Ivan Morozov

Dear Ivan,

Thanks for your response. I really appreciate it. Yes, you are right. It has something to do with the usage of lists. So I changed my equation into:

sol = NDSolve[{q'[t] == (a q[t]^b newefr[t] - q[t]) + (a q[t]^b (newefr[t] - newefr1[t])), q[1] == 0.001}, q, {t, 1, 456}]

where:

newefr = Interpolation[newefrain, InterpolationOrder -> 1]; where: newefrain = Table[rainfun[t]*ff, {t, 1, 456}]

similarly to newefr1:

newefr1 = Interpolation[newefrain1, InterpolationOrder -> 1]; where: newefrain1 = Table[rainfun[t]*ff1, {t, 1, 456}]

And it works! Thanks for your help!

Best Regards, Intan
POSTED BY: INTAN SUPRABA
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