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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0
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0answers
53 views

Solving a complicated integro-differential equation

I'm trying to solve the integro-differential equation: $-(1+z) H(z) \frac{d f_{i}}{dz} = J_{i}(E',z) - f_{i} \sum_{j} n_{\nu_{j}} \sigma_{ij}(E',z) + \int_{E'}^{\infty}dE~\sum_{j,k}f_{k} n_{\nu_{j}} ...
1
vote
1answer
48 views

How to solve an iterative integral equation for a function in Mathematica 8.0?

I would like to solve the following iterative integral equation in order to find the functional form of $P_{0}(k)$ numerically and then use it subsequently for the rest of my code: ...
2
votes
1answer
92 views

Dog chases his tail ! - “parametric differential/Integral equation”..?

I have the following situation where I am interested in the function $m(t)$ $$ \frac{dm}{dt}=4T(t)^{3}+T(t)^{2} $$ $$ T(\tau)=T_{0}-\int_{0}^{\tau}(\frac{dm}{dt})dt*Q_{S} $$ Is there a way to solve ...
0
votes
1answer
64 views

Solve for Joint Distribution Function

I wish to find a joint PDF $h(p,b) $or CDF $H(p,b)$, given the following expression: $(1-L) r \int _0^r\int _0^{\frac{p}{1-L}}h(p,b)dbdp- r L \int _0^r\int _0^{\frac{p-r}{1-L}+\frac{r}{L}}h(p,b)dbdp=...
0
votes
0answers
54 views

Solving a Volterra type (second) integral

I am trying to numerically solve this Volterra type integral equation. The equation I'm plugging in is a simplified version of We will take $H(\eta')$ and $q(\eta)$ to be 1 for now. $\mu$ is = $\...
0
votes
1answer
86 views

How to solve a system of integral equations [closed]

I am trying to solve a system of equations as follows... f1[t]/3 == (1/3)[Integrate[f3[t], t]] f1[t]/(6/5) == Integrate[f2[t], t] f3[t] == Integrate[f1[t], t] I ...
2
votes
2answers
77 views

Integral equation solving

So there is this equation that I have to numerically solve for T: Q/(3nRT) = f(T/300) - f(T/77) Here Q = 920.364, n = 0.24, R = 8.314 while f is defined as the ...
0
votes
1answer
60 views

How do I solve a nonlinear Fredholm integral equation?

$u(x)= 1/3+\int_{0}^{1}x\,t\sqrt{u(t)}\,dt$ u[x] == 1/3 + Integrate[x t Sqrt[u[t]], {t, 0, 1}] Any ideas on how to treat such a problem with Mathematica ...
0
votes
0answers
42 views

Multiple numerical integrations and green's functions propagation of the solution

I have to solve a system of equations where the coefficients have to be computed from numerical integrations. My problem is that my codes is to extremely slow because I each time that it has to ...
0
votes
0answers
94 views

Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
0
votes
0answers
99 views

Solving system of Fredholm integral equations of the second kind

How can we generalize the code previously introduced to solve the Fredholm equation of the second kind to the case of a system of Fredholm integral equations of the second kind? $$ f_{1}(x)-\lambda_{...
3
votes
2answers
71 views

Solving an integral equation for upper boundary

I am reading a paper on High Harmonics Generation (HHG) and a Lewenstein model The paper is here. I would like to reproduce some results but I am stuck at the following problem. I have: $$p(\tau_b,\...
1
vote
0answers
59 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
0
votes
1answer
133 views

Solve a function to find the optimum value of parameter in mathematica [duplicate]

I have a complicated function as shown It doesn't have a standard integration as far as I know. Now, numerical integration of the left hand side function over a set of points gives the right hand ...
2
votes
0answers
46 views

NDSolve with NIntegrate [duplicate]

I'm new to Mathematica and I'm trying to use it to solve some equation like: NDSolve[x'[t]+NIntegrate[x[tau],{tau,0,t}]==20,x,{t,0,10}] But it keeps giving me ...
1
vote
0answers
175 views

Numerical solution to integral equation

I have an integral equation where one factor $f(t)$ in the integrand is defined in terms of an integral equation where it is again a factor. $\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + h[t]$...
8
votes
2answers
566 views

How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
2
votes
1answer
192 views

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 ...
0
votes
0answers
61 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
0
votes
1answer
68 views

Problems with a constant term in an Integrate command

When asking Mathematica to integrate a function with Integrate, I'm getting drastically different results depending on whether I have a proportionality constant ...
1
vote
2answers
196 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
1
vote
1answer
136 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at ...
-1
votes
1answer
180 views

Center of gravity of a cylinder in 3D space [closed]

am trying to find the center of gravity coordinates of a cylinder(x,y,z coordinates). however,I cannot figure it out using the triple integral method especially when it comes to the integral bounds. ...
0
votes
1answer
263 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
2
votes
1answer
184 views

Complex Integration

There are some sequential functions: ...
5
votes
1answer
186 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?
0
votes
2answers
66 views

Simplify integration result with conditions

Let's say I have integral Integrate[1/(1 + (f^2/B^2)), {f, 0, Infinity}] The result is $$\text{ConditionalExpression}\left[\frac{\pi }{2 \sqrt{\frac{1}{B^2}}},\...
5
votes
1answer
408 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
1
vote
2answers
143 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...
2
votes
0answers
196 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
1
vote
1answer
100 views

symbolic integration of product of hankel function and trignometric function

I want to perform the following integration. my function is : r*cos(r)hankel(0,kr) i want to integrate from 0->pi , and want to get the expression in terms of k. I used this command ...
0
votes
1answer
195 views
4
votes
2answers
187 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
1
vote
0answers
175 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times [0,...
1
vote
1answer
610 views

Solving Fredholm Equation of the first kind [duplicate]

I want to numerically solve Fredholm integral equations of the first kind, equations of the form $$g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s$$ where we know the functions $K(t,s)$ and $g(t)$ and seek to ...
4
votes
0answers
415 views

Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: f[t_] = Sqrt[1 + E^(-2 t)] ...
1
vote
1answer
125 views

Is this integral solvable?

I am trying to solve the below mentioned integral. Is it possible to solve this with mathematica. If not, can I get an approximation for this by introducting the variable not to take certain values ? ...
6
votes
3answers
424 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
4
votes
2answers
70 views

DSolve results not what expected

I have the following formula: s'[t] == 230.94 Tan[0.914743 - 0.138564 t] When I solve this by hand I get: ...
1
vote
0answers
117 views

Long running time

I gave this data as input: ...
0
votes
1answer
124 views

Problem with integral equations

I have solved an integral equation with the following methods: ...
4
votes
1answer
452 views

Fredholm integral equation of the second kind with kernel containing Bessel and Struve functions

I need to solve this Fredholm integral equation of the second kind: f[s]+integrate[f[t] K[s,t],{t,0,1}]=s where 0<=s<=1...
1
vote
2answers
82 views

Integral too slow and with conditionals

When I try to solve this integral: $$\int_{-a}^a \frac{x}{\left(x^2+y^2\right)^{3/2}} \, dy$$ it's return ...
0
votes
1answer
113 views

Calculate integral in limit of very large coefficient

How I can calculate following integrals for large values $\alpha$ in Mathematica: $$ I_1 =\int_{0}^{y} \exp\left(\, -\alpha \sqrt{x(1-x)}\,\right)\, {\rm d}x $$ $$ I_2 =\int_{0}^{y} \exp\left(\, -\...
2
votes
1answer
125 views

How to solve an operator form of an integral equation by iteration method?

How I can obtain the $n^{th}$ approximation of the following Operator form integral equation? $F(t)=A(t)+\int_0^tds B(s)F(s)$, where $A(t)=\bigg{(}\begin{matrix}t&0\\Cos(t)&1 \end{matrix}\...
4
votes
3answers
542 views

How to solve an integral equation by iteration method? [duplicate]

How I can obtain $n^{th}$ approximation of the following equation $f(t)=t+\int_0^tds f(s)$ by iteration method?
0
votes
1answer
78 views

Compute integral symbolically

I want to compute the following integral: ...
2
votes
2answers
447 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = \int_0^\...