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.

35 questions with no upvoted or accepted answers
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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
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754 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)] ...
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0answers
145 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?
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62 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
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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
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0answers
96 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
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0answers
274 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
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0answers
365 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. $\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + h[t]$...
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0answers
354 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
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491 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
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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? ...
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0answers
59 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 ...
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52 views

Strange Integral Calculation With Traditional Form

I must be doing something wrong. I define the following integral: The code: ...
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0answers
121 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, ...
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92 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 ...
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90 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 ...
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117 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, ...
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0answers
173 views

Solving a Volterra integral equation

I review this question Solving a Volterra integral equation numerically. But I can not understand that. I have the following code: ...
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0answers
235 views

How to use Halton sequence in Quasi Monte-Carlo integtation

I am trying to use Halton sequence numbers for MC estimator for rendering equation. At the moment I pass one instance of .Net Random object and get next number every time using same object thought the ...
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0answers
100 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 ...
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0answers
390 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,...
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159 views

Long running time

I gave this data as input: ...
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0answers
684 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, ...
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1answer
179 views

How to solve this differential equation analytically?

How can I DSolve the following differential equation? Is there an analytical answer to this equation? ...
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0answers
38 views

Calculate a definite integral containing an ExpIntegral

I need to calculate the following integral Integrate[Exp[-(y/bn)] (-y)^c ExpIntegralE[d, p y], {y, 0, z/x}] Where $z<0,z\in \mathbb{R}$, $x\in\mathbb{R},x>...
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26 views

Using `Integrate` and or `FourierTransform`

I have some general questions about Integrate and FourierTransform. Firstly with ...
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0answers
41 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 ...
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49 views

Get Integral Result without Assumptions

I have the following two functions: ...
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70 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
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0answers
133 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 ...
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0answers
127 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
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0answers
44 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
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0answers
251 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/...
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279 views

Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
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40 views

Nonlinear integral equation — numerical solution

I am trying to solve numerically the following nonlinear integral equation: $\qquad \int_{0}^{x}\left( \frac{y}{x}\right)^{f(y)-1}g(y)\,dy=h(x)$, or ...