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

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)



Thank you in advance!


Please Wait...