Question: How to numerically solve a system of linear ODEs with an external, tabulated source?

Dear Community,

I have a four compartment flow model described with the following system of linear ODEs:

diff(L[1](t), t) = L[2](t)/T[21] - L[1](t)/T[12]

diff(L[2](t), t) = L[1](t)/T[12] - L[2](t)/T[21] + L[3](t)/T[32] - L[2](t)/T[23] + Q(t)

diff(L[3](t), t) = L[2](t)/T[23] - L[3](t)/T[32] + L[4](t)/T[43] - L[3](t)/T[34]

diff(L[4](t), t) = L[3](t)/T[34] - L[4](t)/T[43]

(For easier readability I’ve also described the problem in the attached FourCompartmentModelDescription.docx Word file.)

The time constants are as follows:

T₁₂ = 23.1481 d

T₂₁ = 5.4537 d

T₂₃ =  9.752 d

T₃₂ = 14.9007 d

T₃₄ = 8.8235 d

T₄₃ = 363.7255 d

Initial conditions are as follows:

L₁(0) = 2500.

L₂(0) = 589.

L₃(0) = 900.

L₄(0) = 37100.

Simulation should run from 0 to 400 d.

Could you pls. help me, to solve it numerically in Maple? As a solution I would need L₁(t), L₂(t), L₃(t) and L₄(t) both numerically and graphically. I used Maple to solve ODEs previously, but this time I don’t know, how to correctly specify the problem with an external, tabulated source. I’ve also prepared and attached a Maple worksheet, but did not try to run it yet. (FourCompartments.mw). The external Q(t) source for compartment 2 is attached as Source.xlsx. Should I've forgotten something, pls. let me know.

Your kind help is appreciated in advance,

best regards

Andras

MaplePrimesFourCompartmentModelDescription.docx

FourCompartments.mw

Source.xlsx