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How do you reformulate an integral as an ode-problem?
Differentiate both sides of the equation? Or do you mean something else? :/
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
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
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):
\int_a^b m(x, y) dx = [f(x, y)]_a^b = f(b, y) - f(a, y) = M(y)
But I want to reformulate this integral to an ode-problem
well I think the only way you can do that is like Nylex said, like this:
\frac{d(\int_a^b m(x, y) dx)}{dy} = \frac{dM(y)}{dy}
:redface:
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.
matt grime
Nov8-04, 06:50 AM
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:
\int_0^xf(t)dt = y
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.
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...
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)
Do you mean that the initial value is f(a). Then
ode45(@f, [a, b], y0)
should yield the same value as
QUADL(@f,a,b);
but it dont.
I want them to yield the same value...what am i doing wrong...
I think the inital value should be f(0)
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