Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.
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Questions tagged [integral-equations]
341 questions
8
votes
2 answers
Why can't Mathematica solve this definite integral?
I want to solve the integral
$\int_{p_0}^{p_1}\left(T_0+\Gamma_p(p_0-p)\right)\frac{1}{p}dp$
Mathematica can do the indefinite integral immediately:
>>> Integrate[(T + Γ (p0 - p))*(1/p), p]
-p Γ + (T + p0 Γ) Log[p]
But addind bounds suddenly makes…
pretzlstyle
- 233
- 1
- 5
8
votes
5 answers
Functional fixed points (ie fixed point of mapping from function space C[0,1] to itself)
I am looking for some tips or guidance as to what machinery in mathematica can help me get at this problem numerically. I am looking for fixed points of a mapping, but the objects in question are themselves functions. Hence I am looking for a fixed…
user434180
- 181
- 2
6
votes
1 answer
Is there a syntax that allows Mathematica to solve integral equations?
Is there syntax that causes Mathematica solve integral equations like the one below (I know that I can transform it to a differential equation. However, I would like to know if Mathematica solves equations in integral form.)?
$$
\int_{r_0}^{x} f(z)…
Alan Jenkins
- 63
- 3
5
votes
1 answer
Recursive Integration
I'd like to evaluate the following recursive integration using Mathematica
$$
\ M(T) = \int_0^T\int_0^\infty e^{-\delta s}g(x,s)dxds\ +\int_0^T e^{-\delta s}f(s)M(T-s)ds\,
$$
where $g(x,s)$ and $f(s)$ are statistical probability density…
SNMRamli
- 123
- 7
4
votes
0 answers
Non-linear integral equation
I'm trying to solve with Mathematica an integral equation. I found this excellent answer (How to solve a non-linear integral equation?) solving with a collocation method a problem which can be restated as:
$$ \int_a^b f \left( \phi \left(x \right)…
zakk
- 978
- 1
- 7
- 17
4
votes
3 answers
How to find the area locked between two curves and a line
I need to find the area which is locked between these two curves and a line(the darker area). I have all three equation both curves and the line.
I want just want to composite the right integral for this operation. I will evaluate the area.
Dimitar Kazakov
- 69
- 2
4
votes
2 answers
How to solve this integral equation using Mathematica?
My question: How do I use Mathematica to find the solution to Case 2? As a cross check for the code, does it verify the solution in Case I?
Case 1: We will look at an easier problem first. Let $|\alpha|, |\beta| \leq \alpha_c, \alpha_c \leq \pi$. I…
user35588
4
votes
1 answer
Solve Fredholm integral equation of the second kind containing Double Exponential Oscillatory
Given
where $h =0.5$ and $\kappa = 1$.
$G_F(s)$ is the Fourier cosine transform of $G(\lambda)$ defined
as
Then I want to solve the following Fredholm integral equation of the second kind for the function $\varphi(s)$ with $s \in [0,1]$:
I…
Wilhelm
- 615
- 3
- 9
2
votes
1 answer
Integral equation
I'm trying to solve the following integral equation:
Integrate[-k/2 Exp[-k Abs[x-z]] f[x], {x,0,d}] == a f[z]
Differentiating twice with respect to z should yield the following differential equation if i'm not mistaken (using Leibniz integral…
Noel
- 291
- 1
- 7
2
votes
2 answers
Integrate takes too long without output
I am trying to evaluate this integral but it takes too long without results.
Integrate[1/(x^2 + y^2 + z^2)^(3/2), {x, -L/2, L/2}, {y, -W/2, W/2}]
and $(W, L, z)> 0$ However, not specifying the limits gives results
In[411]:= Integrate[1/(x^2 +…
MMA13
- 4,664
- 3
- 15
- 21
2
votes
1 answer
Inconsistent results of integration that include the Floor[] function
I had thought that with the following two integrals, I was simply expressing the same idea in two different but equivalent ways, with the range of the values (excluding x) within the Floor[] term being, in both instances, in the interval [100,101).…
CrimsonDark
- 249
- 1
- 6
2
votes
1 answer
Computational limit reached for an integral equation calculation
I have trouble running a calculation without getting an error,
I have the given Fredholm equation:
where $\psi(x)=\sin x$and $K(x,y)=\cos(x/2-3y)$
Now I calculated that for the operator to be a contraction, $\lambda<\sqrt{2}$. Further, I have…
Vangsnes
- 591
- 2
- 9
2
votes
0 answers
Is Mathematica able to solve 2D Volterra integral equations?
I have a 2D linear non-homogeneous Volterra integral equation of the second kind that I am painfully trying to solve. Here is my equation:
$L_o(x,y) = L_e(x,y) + \frac{1}{\pi} \int_0^{2\pi} \int_0^{\theta_\text{max}(x,y,\phi)} L_o(x+h \tan \theta…
Balfar
- 55
- 5
2
votes
1 answer
How to integrate exponential function over implicit function
The following integral can be solved in Mathematica:
Integrate[Exp[a*(z - 1)], {x, y, z}\[Element]Sphere[],Assumptions -> a > 0 && a\[Element]Reals]
Outputs:
But if I change Sphere[] to implicit function, the integral can not be…
Chris Guo
- 149
- 8
2
votes
1 answer
A two-dimensional non-linear integral equation
I'm trying to figure out the solution to the integral equation
$$\frac{1}{2}xyf(x,y) - \int^1_0\int^1_0\left[\frac{\exp[1 - f(x,y)]}{(\exp[1 - f(x,y)] + \exp[1 - f(x',y')])^2}\right]dx'dy'=0$$
First, is this a viable question?
and if yes, How can I…
이말러
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