I have a function beta defined as an integral. I want to define another function alpha "being the integral of that function".

In particular I want to solve the differential equation d alpha(s)/ds = 1/2* beta(s)^2 and get the function alpha. Beta is defined as follows:

fun1=@(x) -exp((-c*x*b+a*exp(-b*x)-a)/b); beta=@(k) (exp(-(-c*k*b+a*exp(-b*k)-a)/b)*integral(fun1,0,k)); The problem is that I can't for example do something like alpha= @(x) integral(beta,0,x)

Answer 1

[Torsten]

Solve

d(alpha)/ds = 0.5*(exp(-(-c*s*b+a*exp(-b*s)-a)/b)*y)^2
dy/ds = -exp((-c*s*b+a*exp(-b*s)-a)/b)

alpha(0) = alpha0 
y(0) = 0

using an ODE integrator.

Best wishes

Torsten.

[giorgione palma]

thanks for your answer but I was more thinking about computing the integral rather than solve an ODE. I think there must be a way to compute the numeric integral such fun= @(t) int(f(s) * int(g(z), z == (0..s)), s == (0..t))

[Torsten]

Computing an integral is the same as solving an ODE...

Best wishes

Torsten.