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.

42 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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0answers
928 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
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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
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0answers
177 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
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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
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0answers
482 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
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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
54 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
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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
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0answers
51 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
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0answers
76 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
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0answers
315 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
368 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
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0answers
447 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
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0answers
502 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? ...
1
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0answers
110 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}}{\...
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0answers
59 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 ...
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0answers
160 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 -...
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55 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
171 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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112 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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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 ...
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0answers
156 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
331 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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0answers
107 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
160 views

Long running time

I gave this data as input: ...
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0answers
704 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
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1answer
44 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 ...
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0answers
37 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 ...
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0answers
25 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 ...
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0answers
75 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*!( ...
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70 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 ...
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0answers
68 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 ...
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50 views

Using `Integrate` and or `FourierTransform`

I have some general questions about Integrate and FourierTransform. Firstly with ...
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0answers
84 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
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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
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0answers
352 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
144 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
60 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
292 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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0answers
51 views

Gauss quadrature

I need help with this coding question. I'm not sure if I did it wrong or inputted the wrong thing Raw InputForm ...