1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral to ode

  1. Nov 5, 2004 #1
    How do you reformulate an integral as an ode-problem?
  2. jcsd
  3. Nov 5, 2004 #2
    Differentiate both sides of the equation? Or do you mean something else? :/
  4. Nov 5, 2004 #3
    But is that possible if you have an integral between two values. I know its possible if you have an indefinite?! integral...now i have

    M(y)=int(a,b) m(x,y) dx
  5. Nov 6, 2004 #4
    m(x, y) is a function of x and y if you integrate this with respect to x you will get a function of y, so that will then be M(y):

    [tex]\int_a^b m(x, y) dx = [f(x, y)]_a^b = f(b, y) - f(a, y) = M(y)[/tex]
  6. Nov 6, 2004 #5
    But I want to reformulate this integral to an ode-problem
  7. Nov 6, 2004 #6
    well I think the only way you can do that is like Nylex said, like this:

    [tex]\frac{d(\int_a^b m(x, y) dx)}{dy} = \frac{dM(y)}{dy}[/tex]
  8. Nov 8, 2004 #7
    But with this I still need to solve the integral, dont I?
    And I want to rewrite it as an ode so i dont have to solve the integral.
  9. Nov 8, 2004 #8

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    From your posts it isn't clear if y is a function of x or not, since it usually isn't that the integral has limits a and b.

    An integral that can be turned into a differential (ODE) would be something like:

    [tex]\int_0^xf(t)dt = y[/tex]

    which has associated differential equation dy/dx = f(x)

    so why do you even think that the type of equation you wrote has an ODE equivalent?

    Even if y were a function of x, then the integral you wrote would still only yield a number, and that isn't the function y.
  10. Nov 8, 2004 #9
    y isnt a function of x. a and b are reell numbers.
    The question in the book is(numerical analysis)

    M(y)=int(a,b) m(x,y) dx
    a. Use quadl in matlab to determine M
    b. An alternative way to determine M is to rewrite the integral as an ODE-problem. Do that and use ode45 in matlab to solve the ode-problem. Compare with the solution in a.

    b is really strange...
  11. Nov 8, 2004 #10
    what ode45(f, [a, b], y0) does is simply integrating f from a to b, using inital value y0...

    so you can use that to get your answer (you will need to use the @ again ;-), like this ode45(@f, [a, b], 0)
  12. Nov 9, 2004 #11
    Do you mean that the initial value is f(a). Then
    ode45(@f, [a, b], y0)
    should yield the same value as
    but it dont.
    I want them to yield the same value...what am i doing wrong...
  13. Nov 9, 2004 #12
    I think the inital value should be f(0)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook