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Question: Differential system of equations taking to long to solve

Question:Differential system of equations taking to long to solve

merinoises 20 Maple
ode dsolve numeric ivp differential-equations
January 01 2023
1

Hello everyone,

I am having trouble with this a system of 12 differential equations with the respective 12 initial conditions. I try to usen dsolve with the "numeric" parameter but it stays "evaluating" forever. I tried a system of 10 equation and I got the correct answer, although the program stayed calculating for several minutes (more or less 5 minutes). Is the size of this system too much to handle for the program? 

This is the system of differential equations (sys) and the initial conditions (ics) that I am trying to solve:

maple_primes_question.mw

sys := {diff(a[0](t), t)-(diff(a[1](t), t))+diff(a[2](t), t)-(diff(a[3](t), t))+diff(a[4](t), t)-(diff(a[5](t), t)) = 0, diff(b[0](t), t)+diff(b[1](t), t)+diff(b[2](t), t)+diff(b[3](t), t)+diff(b[4](t), t)+diff(b[5](t), t) = 0, diff(a[0](t), t)-.8090169943*(diff(a[1](t), t))+.309016994*(diff(a[2](t), t))-16*a[2](t)+.3090169950*(diff(a[3](t), t))+77.66563145*a[3](t)-.809016994*(diff(a[4](t), t))-187.3312629*a[4](t)+1.000000002*(diff(a[5](t), t))+289.4427191*a[5](t) = 0, diff(a[0](t), t)-.3090169938*(diff(a[1](t), t))-.8090169951*(diff(a[2](t), t))-16*a[2](t)+.8090169933*(diff(a[3](t), t))+29.66563140*a[3](t)+.3090169967*(diff(a[4](t), t))+27.33126306*a[4](t)-1.000000000*(diff(a[5](t), t))-110.5572808*a[5](t) = 0, diff(a[0](t), t)+.3090169938*(diff(a[1](t), t))-.8090169951*(diff(a[2](t), t))-16*a[2](t)-.8090169933*(diff(a[3](t), t))-29.66563140*a[3](t)+.3090169967*(diff(a[4](t), t))+27.33126306*a[4](t)+1.000000000*(diff(a[5](t), t))+110.5572808*a[5](t) = 0, diff(a[0](t), t)+.8090169943*(diff(a[1](t), t))+.309016994*(diff(a[2](t), t))-16*a[2](t)-.3090169950*(diff(a[3](t), t))-77.66563145*a[3](t)-.809016994*(diff(a[4](t), t))-187.3312629*a[4](t)-1.000000002*(diff(a[5](t), t))-289.4427191*a[5](t) = 0, diff(a[1](t), t)+4*(diff(a[2](t), t))+9*(diff(a[3](t), t))+16*(diff(a[4](t), t))+25*(diff(a[5](t), t))-3*(diff(b[1](t), t))+12*(diff(b[2](t), t))-27*(diff(b[3](t), t))+48*(diff(b[4](t), t))-75*(diff(b[5](t), t)) = 0, diff(b[0](t), t)-.8090169943*(diff(b[1](t), t))+.309016994*(diff(b[2](t), t))-48*b[2](t)+.3090169950*(diff(b[3](t), t))+232.9968944*b[3](t)-.809016994*(diff(b[4](t), t))-561.9937886*b[4](t)+1.000000002*(diff(b[5](t), t))+868.3281572*b[5](t) = 0, diff(b[0](t), t)-.3090169938*(diff(b[1](t), t))-.8090169951*(diff(b[2](t), t))-48*b[2](t)+.8090169933*(diff(b[3](t), t))+88.99689421*b[3](t)+.3090169967*(diff(b[4](t), t))+81.99378917*b[4](t)-1.000000000*(diff(b[5](t), t))-331.6718425*b[5](t) = 0, diff(b[0](t), t)+.3090169938*(diff(b[1](t), t))-.8090169951*(diff(b[2](t), t))-48*b[2](t)-.8090169933*(diff(b[3](t), t))-88.99689421*b[3](t)+.3090169967*(diff(b[4](t), t))+81.99378917*b[4](t)+1.000000000*(diff(b[5](t), t))+331.6718425*b[5](t) = 0, diff(b[0](t), t)+.8090169943*(diff(b[1](t), t))+.309016994*(diff(b[2](t), t))-48*b[2](t)-.3090169950*(diff(b[3](t), t))-232.9968944*b[3](t)-.809016994*(diff(b[4](t), t))-561.9937886*b[4](t)-1.000000002*(diff(b[5](t), t))-868.3281572*b[5](t) = 0, diff(a[0](t), t)+diff(a[1](t), t)+diff(a[2](t), t)+diff(a[3](t), t)+diff(a[4](t), t)+diff(a[5](t), t)-(diff(b[0](t), t))+diff(b[1](t), t)-(diff(b[2](t), t))+diff(b[3](t), t)-(diff(b[4](t), t))+diff(b[5](t), t) = 0}

ics := {a[0](0) = 0.7499999990e-1, a[1](0) = .1500000001, a[2](0) = .1500000002, a[3](0) = .1500000000, a[4](0) = .1499999999, a[5](0) = 0.7499999987e-1, b[0](0) = .9750000000, b[1](0) = 0.5000000005e-1, b[2](0) = -0.5000000005e-1, b[3](0) = 0.5000000000e-1, b[4](0) = -0.4999999998e-1, b[5](0) = 0.2499999996e-1}
sols := dsolve(`union`(sys, ics), numeric)

Download maple_primes_question.mw

What am I doing wrong? or is it that the program cannot handle such a large system? In that case, that would be dissappointing since I have to solve a similar system but with up to 22 differential equations and initial conditions so I am stuck...

Anyway, thank you very much for any guidance, and happy new year.
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