Questions tagged [integral-equations]
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.
45
questions with no upvoted or accepted answers
8
votes
0answers
2k views
Using NDSolve for Integro-Differential Equations
I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are:
$\dot{x}=\big|y(t)-x(t)\big|^{1/n}\left[\text{Sign}[y(...
5
votes
0answers
945 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)]
...
3
votes
0answers
114 views
Can this integral equation problem $\int_\Gamma \frac{e^{ik|x-y|}}{4\pi|x-y|}\varphi(y) \, \mathrm{d} y = u_{x_0}^{in}(x)$ be solved?
I am not sure if Mathematica is capable of solving integral equations in 2D/3D. I found this page in the documentation, but this is just for 1D.
The following is what I would like to solve, it can ...
3
votes
0answers
182 views
How can I solve a nonlinear fractional order integro-differential equation?
How do I solve the nonlinear fractional order integro-differential equation shown above in Mathematica?
3
votes
0answers
66 views
2-dimensional formatting for integration
So I am trying to integrate the function x^2 * Sin^2[n Pi x / a], {x,0,a}.
The code I am using is in the "two-dimensional formatting" of mathematica: I am using Esc ...
3
votes
0answers
492 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.
$\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + h[t]$...
3
votes
0answers
135 views
What can I do to improve the performance of my calculations?
I'm trying to express a simple probability problem in Mathematica, but am having trouble getting my calculations to execute at a reasonable speed.
I have an object whose unknown location is modeled ...
2
votes
0answers
56 views
How to get Integrate to determine units
In a similar fashion to the question asked here, I am having trouble trying to get Integrate to correctly determine the units of the integrand:
Here I have plugged in specific values into the general ...
2
votes
0answers
57 views
Computing integral using trapezoid method and simpsons' rule for a given partition
I am given f[x_]=E(x^-x)-1 on interval [1,4] and partition ...
2
votes
0answers
58 views
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 ...
2
votes
0answers
77 views
Solving a finite Hilbert transform from 2D thin wing theory
I have a problem where I know $w(x) =1$ and want to find $u(x)$. It's a well-known problem I am recreating, from a 1972 paper. Note the paper doesn't solve the problem, the integral equation, it just ...
2
votes
0answers
321 views
Data fitting with differential equation and non analytical integral
I would like to fit a set of data (measured value vs time) with a model that contains a differential equation and an integral that has to be evaluated numericaly. The integral also contains Bessel ...
2
votes
0answers
375 views
Volterra integral equation
I have to find an approximate numerical solution for the equation
$$
F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x)
$$
$$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$
...
2
votes
0answers
457 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,...
2
votes
0answers
503 views
Code for solving numerically an integro-differential equation
First of all, I want to greet the community. This is my first question, but I hope I will be able to help answering others members questions, although I am quite new working with Mathematica.
I would ...
2
votes
0answers
1k views
Integro-differential equation with double integral
I am looking at the following variation of a integro-differential, with y[0]=1.
The output is not great, any solutions to this?
...
1
vote
0answers
44 views
NDSolve to solve 2D space 1D time partial integro-differential equations
I have a set of pdes in 2D space and 1D time, one of them is related to the integral in space by Reynolds function. The equations are similar to
$$\frac{\partial \phi}{\partial t}=-\frac{\partial \...
1
vote
2answers
51 views
Error when integrating with constants?
I'm trying to integrate an ellipse: (x^2)/alpha^2) + ((y^2)/beta^2) = 1. I am not sure if I should have insert constants for alpha and beta or if there's a way to keep them there.
This is my code
<...
1
vote
0answers
111 views
Solving the following system of integrodifferential equations: speed up of the code
Consider a system of equations
$$
\begin{cases}\frac{\partial f(E,t)}{\partial t}-H[T_{\gamma},f(E,t)]E\frac{\partial f(E,t)}{\partial E} -I[f(E,t),E,T_{\gamma}(t)]=0, \\ \frac{\partial T_{\gamma}}{\...
1
vote
0answers
61 views
NDsolve Boundary Condition is a Function of the Solution
I am trying to solve something like Fick's Law using NDSolve:
$$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$
Subject to a ...
1
vote
0answers
169 views
How to solve ode with convolution?
my question is as this and i want to get the solution of this ode x(t)
$
({M_{33}}{\rm{ + }}{{\rm{m}}_{33}})x''(t) + \int\limits_{ - \infty }^t {x'(tau){K_{33}}(t -...
1
vote
0answers
55 views
Strange Integral Calculation With Traditional Form
I must be doing something wrong.
I define the following integral:
The code:
...
1
vote
0answers
172 views
I need to solve integro–differential equation with derivative
There are 2 equations a1 and a2, the difference between them is the red words part(integral term).
Boundary x(0)=0,x'(0)=0
x'(t-u) means Bring t-u into the derivative of x ，for example, if x(t)=t^3, ...
1
vote
0answers
114 views
Nonlinear vibration
I am trying to solve this equation:
with the following constants:
alpha1=3.7
alpha2=3.84
Nnon=0.0009
Cnon=0
VDC=2
VAC=0.6
The solution should be as shown in the ...
1
vote
0answers
134 views
Can Mathematica do a Double Path Integral?
I've obtained some analytical results that I'd like to verify numerically by doing a double path integral. I haven't done this before with Mathematica and am unsure if it's possible, I'd like to do ...
1
vote
0answers
160 views
Solving a cumulative distribution from a first order condition
I could use some guidance in using Mathematica's NDSolve. I'm attempting to numerically uncover a cumulative distribution function (CDF), $F(p)$, with density $f(p)$ from a first order condition, ...
1
vote
0answers
340 views
Solving Fredholm equation of the 2nd kind
While I was using the code from here to solve this integral equation:
...
1
vote
0answers
108 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 ...
1
vote
0answers
161 views
1
vote
0answers
705 views
Testing the convergence when solving an integral equation
I am trying to find the solution of an integral equation such that a certain convergence criterion is fulfilled.
Now the problem is that the function doesn't look like what I am actually expecting, ...
0
votes
0answers
32 views
Integral of functions within functions
I define the function Rho, use it in an integration command, store that result as a new function M, then write functions P and Rho1 in terms of M and Rho, and finally integrate Rho1 and store that as ...
0
votes
0answers
52 views
Problems with the output of the integral function
I write here because I've some problems when I want to integrate this quantity with respect to z:
rH, a and z are real values, being TT4 a real value too and I especify that in the assumptions of the ...
0
votes
1answer
72 views
How can I change the dependent variables of a function?
What I want is to define a function which depends of some variables and then get the expression for that same function when it depends of different variables.
My specific case is: (where ...
0
votes
0answers
43 views
Wolfram alpha query works online but not through mathematica?
Bit of a bizarre problem I'm having (well, more a question than a problem). I am trying to solve an integral, which I queried using the online wolfram alpha website. The input and output are ...
0
votes
0answers
44 views
Solving coupled integro-differential equations using Laplace transform
I have two coupled integrodifferential equations, as shown in the image attached.
I am trying to solve them using a Laplace transform, as follows
...
0
votes
0answers
78 views
How to solve this equation with Duhamel integral?
How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve & LaplaceTransform But nothing works
x[t] == -0.3375*!(
...
0
votes
0answers
76 views
Solving partial differential equations has integral terms
Recently, I met a partial differential equation with integral term. At first, I wanted to solve it directly through NDSolve, but found that it was not feasible because MMA could not directly deal with ...
0
votes
0answers
90 views
the number of equation does not match the number of variables
Excuse me , can you help me , please ?
When i make run for this programme it give me a wrong that the number of equations does not match the number of variables ,,,, I try a lot on finding the wrong ...
0
votes
0answers
53 views
Using `Integrate` and or `FourierTransform`
I have some general questions about Integrate and FourierTransform. Firstly with ...
0
votes
0answers
92 views
Integral of intersection of a spiral and a circle
I need to prove that for a full turn of a logarithmic spiral (independent from the constant tangent of it) and a straight line on the z axis, the logarithmic spiral always covers more space-time in ...
0
votes
0answers
76 views
How to write code for replacing result in integral
I have about 100 integral term, the general form of them is as follows:
$$\int \int dx~dy~N_\mu(x)~N_\nu(x)~F(x,y)~A_\nu(y)$$
For each $\mu$ and $\nu$, the definition of functions are different.
I ...
0
votes
0answers
408 views
Multiple variable integration of a function of multiple variables
I'm having trouble writing code in Mathematica for this multi variable integration:
$\int_0^1\int_0^1...\int_0^1F[x_1,x_2,...,x_n]dx_1dx_2...dx_n$
If I already know the number of elements of A it is ...
0
votes
0answers
145 views
Solving (numerically) integro-differential equation
I am absolutely new to Mathematica, and I installed it to solve a specific equation describing dopamine diffusion in cerebral tissue. I get a number of mistakes (boundaries for a start), but I was ...
0
votes
0answers
62 views
NIntegrate::inumr Error For Multiple NIntegrate Operations
I would like some help trying to use Mathematica (I just started using it!) to compute the numerical integration of a complicated function (assigned "longitudinalWake" in this example). Essentially, I ...
0
votes
0answers
293 views
Solving Integral equation by iteration
I am trying to solve coupled integral equation by iteration following the procedure that has been discussed in http://www.mathematica-journal.com/issue/v9i2/contents/IntegralEquations/...
