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Question: Where does this difference between formal and numeric dsolve come from?

Question:Where does this difference between formal and numeric dsolve come from?

mmcdara 6149 Maple 2015
ode dsolve numeric differential-equations
April 10 2020
2

Hi, 

I have a 2nd order linear ODE that I solved firstly in a formal way.
The plot of the solution contains a "hole" which, in fact, corresponds to the range where the formal solution is not real.
This seemed strange to me as I expected a real solution.
So I solved this ODE numerically and this gave me a real solution.
Could you please explain that to me ?

Thanks in advance

PS : These results are obtained with Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895

> 

restart:
> 

with(plots):
> 

perturbation := .9*(diff(epsilon(t), t, t)) = (-28.67085587*piecewise(0.2000000000e-1*t < 0.8e-1, 0., 0.2000000000e-1*t < .12, -0.8e-1+0.2000000000e-1*t, 0.2000000000e-1*t < .14, .16-0.2000000000e-1*t, 0.2e-1)-0.7645561571e-1*t-1.548363347)*(diff(epsilon(t), t))-0.7596363e-1*piecewise(0.2000000000e-1*t < 0.8e-1, 0., 0.2000000000e-1*t < .12, -0.8e-1+0.2000000000e-1*t, 0.2000000000e-1*t < .14, .16-0.2000000000e-1*t, 0.2e-1)-0.202569683e-3*t+0.26997403e-1-10.10*epsilon(t)

perturbation := .9*(diff(`&epsilon;`(t), t, t)) = (-28.67085587*piecewise(0.2000000000e-1*t < 0.8e-1, 0., 0.2000000000e-1*t < .12, -0.8e-1+0.2000000000e-1*t, 0.2000000000e-1*t < .14, .16-0.2000000000e-1*t, 0.2e-1)-0.7645561571e-1*t-1.548363347)*(diff(`&epsilon;`(t), t))-0.7596363e-1*piecewise(0.2000000000e-1*t < 0.8e-1, 0., 0.2000000000e-1*t < .12, -0.8e-1+0.2000000000e-1*t, 0.2000000000e-1*t < .14, .16-0.2000000000e-1*t, 0.2e-1)-0.202569683e-3*t+0.26997403e-1-10.10*`&epsilon;`(t)

 (1)
> 

Digits:=10:
EPS := rhs( dsolve({evalf(perturbation), epsilon(0)=0, D(epsilon)(0)=0}, epsilon(t)) ):

# a lengthy expression that involves Kummer's special functions
> 

plot(EPS, t=0..10, gridlines=true);


Digits:=20:
evalf(eval(EPS, t=5));
Digits:=10:

 

-0.26529838913395427314e88+0.10340147081332027605e89*I

 (2)
> 

numsol := dsolve({perturbation, epsilon(0)=0, D(epsilon)(0)=0}, numeric):

odeplot(numsol, [t, epsilon(t)], t=0..10, gridlines=true, color=red)

 
> 

 


 

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