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Question: How can I solve an ODE numerically, when one of the terms is an integral that can not be solved analytically?

Question:How can I solve an ODE numerically, when one of the terms is an integral that can not be solved analytically?

mlog 10 Maple 18
integral dsolve numeric
June 28 2018
1

Dear Maple primes,

Could you, please, help me with numerical solution of an ODE?

The ODE looks like this

dz/dx = f1(x,z) + f2(z)

where f1(x,z) is some simple function of x and z (that does not create any problem), but f2(z) is given as

f2(z) = int(f3(t), t = z1..z2)

The problem appears, when the integral cannot be solved analytically.

Below is an example of the problem (here I chose the function f3(t)= tt as well as other functions, intervals and initial condition only for the sake of illustration of the problem):

> 

restart; with(plots)
> 

INT := Int(t^t, t = .1 .. z(x), method = _DEFAULT)
> 

eq1 := {diff(z(x), x) = x+z(x)+INT, z(.1) = .1}
> 

plot1 := dsolve(eq1, type = numeric, range = .1 .. 1)
> 

odeplot(plot1)


Download z-for_primes_dsolve.mw

Thank you in advance!

Max
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