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.

38 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
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(...
6
votes
1answer
50 views

Solving the Lotka-McKendrick model with NDSolve

The Lotka-McKendrick model is a demographic model that represents the way a population changes over time due to fertility and mortality. For an age-specific population density $ u(a, t) $, and a total ...
5
votes
0answers
864 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
60 views

Why this change gives different results in Integrate?

I'm new in Mathematica and can't understand why changing a number from Real to Integer is giving different results in my equations: ...
3
votes
0answers
165 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
63 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
445 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
29 views

Numerical solution for an integro-differential equation

I would like to solve numerically the following integro-differential equation $$ \partial_t \rho(t,x) \,=\, \partial_x\big(f'(x)\,\rho(t,x)\big) \int_0^\infty f(\xi)\,\rho(t,\xi)\,d\xi \;+\\ +\; \...
2
votes
0answers
46 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
71 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
110 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 ...
2
votes
0answers
307 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
363 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
424 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
497 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
137 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
41 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 ...
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
159 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
105 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
127 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
144 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
312 views

Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
1
vote
0answers
106 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
160 views

Long running time

I gave this data as input: ...
1
vote
0answers
699 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
27 views

Sum of integrals is not the same as the integral of the sum

I came across this behaviour in integration (note I put b=2 in the end to make sure that MA is not trying to use complex b): <...
0
votes
3answers
109 views
+50

Solving a function inside an integral

I have an integral given by, $$a = c z_s^{d+1}\int_0^1 dx x^d (1-c^2 z_s^{2d} x^{2d})^{-1/2}$$ where $d$ is just the dimension of my choice, say $d=3$, $a$ and $z_s$ are constants (can be between $0-...
0
votes
0answers
34 views

Help with NIntegrate with singularity and variable integration limit

I have a function of the type: $$ F(x,z)= \int_{-\infty}^{\infty} dx' \int^{z}_{-\infty} dz' f(z,z',x,x')\frac{\partial g(z',x')}{\partial z'}$$ where the integration order may be interchanged. I ...
0
votes
0answers
36 views

Using `Integrate` and or `FourierTransform`

I have some general questions about Integrate and FourierTransform. Firstly with ...
0
votes
0answers
71 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
75 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
281 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
141 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
54 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
282 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/...