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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.

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35 views

Multiple Integral Different Notations

I am wondering... what is the difference between these two notations? I am trying to compute: $$ \int_{-\frac{H}{2}}^{\frac{H}{2}}\int_{-\frac{L}{2}}^{\frac{L}{2}}-z a(x) b(x)\mathrm dx\mathrm dz $$...
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0answers
51 views

Strange Integral Calculation With Traditional Form

I must be doing something wrong. I define the following integral: The code: ...
0
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0answers
47 views

Get Integral Result without Assumptions

I have the following two functions: ...
2
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1answer
96 views

Symbolic integration of Exponential

How can I solve this integration? I want to solve this integration with c, B, H, Y, b, w surviving as constants in the result: ...
4
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2answers
150 views

Expansion of the Meijer G Function

I'm trying to do the integral Integrate[ B^2*BesselK[0, ko*ρ]^2*2 π*ρ, {ρ, a, ∞}] which I figured should be relatively simple as the integral of a Bessel ...
4
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0answers
80 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
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2answers
106 views

An integral problem with Sin and Cos

I have a difficulty in calculating the following integral with Mathematica: $\int^{\pi}_{0}d\theta_1\frac{ (\sin\theta_1)^2*(2(2-\cos\theta_1\cos\theta)^2+(\sin\theta\sin\theta_1)^2)}{((2-\cos\...
1
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1answer
83 views

Unable to obtain Analytical expression for a long integral

I have the following parameter c1 that I wish to integrate analytically (I need a close form expression in order to study them in detail): ...
0
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0answers
40 views

Solving a Volterra integral Equation with singularities

Dears, I am trying to solve the equation in the below picture. What I did is: I used wavelet functions and substitute the wavelet instead of u, where I have the ...
2
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1answer
208 views

Solve integro-differential equations

I am trying to numerically solve the following integro-differential equation and get some plots for $n(s)$ vs $s$: $$ \dot{n}(s)-\frac{\dot{w}(s)}{2w(s)}\int_{-\infty}^s ds'\frac{\dot{w}(s')}{w(s')}(...
1
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1answer
58 views

Evaluation of an integral using Mathematica

I am trying to evaluate the following integral, but the result I got is imaginary part. Do you know if there is a way to get a better evaluation of difficult integrals? ...
0
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0answers
62 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 ...
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1answer
197 views

Solving Integro-differential equation numerically with shooting method

This question is related a question I previously asked here Solving integro-differential equation with boundary condition at infinity and for which a solution was found . Now I am dealing with a ...
0
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1answer
38 views

fisrt 5th iterations of a sequence of functions: integro-differential equations [closed]

Please I am struggling to compute with mathematica the first 5th iterations of the sequence of functions $u[n,t]$ satisfying the integro-differential equation Please help me with the code. Patrick
2
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2answers
174 views

How to Integrate the Derivative of a function with Assumptions on the function?

I have a monotonic increasing function g and constant αsuch that ...
1
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0answers
96 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, ...
3
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2answers
252 views

Solving integro-differential equation with boundary condition at infinity

I wish to solve a differential equation that contains a hard-to-evaluate integral and to plot the solution in a range at least $r\in(0,10)$. The equation comes from a Hartree equation (Schroedinger ...
2
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1answer
136 views

How to solve the intergo-differential equation with derivative [duplicate]

I do not know how to handle the integro-term. ...
5
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1answer
423 views

2d catenary in Mathematica

I'm working in Mathematica to plot a 2-d catenary in Euclidean space according to this Math Exchange Link, specified with a square Dirichlet boundary condition. Here's what I've coded using ...
1
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1answer
52 views

How to plot a 2 variable function of an integral?

I have this function: $$E_p(x_0,y_0,t)=E_0e^{-i\omega t}\int^{\frac{a}2}_{\frac{-a}2}\int^{\frac{b}2}_{\frac{-b}2}\frac{e^{ik\sqrt{(x-x_0)^2+(y-y_0)^2+z^2}}}{\sqrt{(x-x_0)^2+(y-y_0)^2+z^2}}dxdy$$ ...
9
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2answers
306 views

Fredholm Integral Equation of the 2nd Kind with a Singular Difference Kernel

After reviewing the literature, I could not find an analytic solution to the equation $$\int^{1}_{0}dx\frac{f(x)}{|x-y|^{2/3}}=cf(y)$$ for $f(y)$, where $c$ is a constant and $y\in[0,1]$. I'm ...
0
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1answer
63 views

Can I make Wolfram Alpha use a specific substitution when integrating? [closed]

Can I define the '$u = \dots$' for an integral? For example when I integrate $\frac{x^3}{\sqrt{6 - x^2}}$ with respect to $x$, the program automatically sets $u = x^2$, how can I change this so it ...
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3answers
193 views

NDSolve Integro-differential equation

I have hard time to solve numerically the following integro-differential equation: ...
2
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1answer
156 views

How do I solve a kind of integral equation with Mathematica?

I would like to prove that only the functions of the form $f(R)\propto 1/R^2$ satisfy the following integral equation (assume $r>r_0>0$): $$ \int\limits_{r-r_0}^{r+r_0}\left({r^2\over{2r_0^2}}-{...
1
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3answers
120 views

integral equation iteration

So I am trying to recreate the numerical treatment in this papir (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.29.130), equation 3.7. The main point is to try to solve the following equation ...
2
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2answers
255 views

How to solve this differential equation with integral?

How to solve this differential equation with integral? $\omega = 1.2;$ $i1 = 25640;$ $ia = 4*10^6;$ $c2 = 1.4513*10^5;$ $t5 = 16000*\cos({\omega*t});$ $tpto = 2.8*10^6*{\theta'}(t);$ $cr(\omega)...
1
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1answer
49 views

Solving linear equation with integrals

I have a simple equation with respect to constants A and B, unfourtunately it's written using definite integrals with unknown ...
1
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0answers
78 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 ...
5
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2answers
239 views

Solving integral equation

How can I solve the following integral equation for $f(x)$ on $x \in [0,1]$? $$ (f(x) -x) \int_0^1 \left( \frac{\mathrm e^{2-2f(x)}}{\left(\mathrm e^{1-f(x)}+\mathrm e^{1-f(y)}\right)^2}- \frac{\...
3
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0answers
124 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?
0
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0answers
64 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 ...
4
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2answers
227 views

How can I solve a 2nd order ODE containing an integral with NDSolve?

I'm trying to solve a equation of gravitional wave propagation given by $$ \chi''(u) + \frac{2}{u} \chi'(u) + \chi(u) = -\frac{24 f_h (u)}{u^2}\int^u_0 \frac{j_2 (u - U)}{(u - U)^2}\chi'(U)\mathrm ...
0
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0answers
47 views

NDSolve with a little bit of NIntegrate and a little bit of Integrate

This equation is for solving neutron flux energy distribution taking upscatter into account (without, you just get C/E, no lie). I've been massaging it and trying various things I've found posted ...
1
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0answers
76 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 ...
0
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0answers
100 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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1answer
58 views

Finding a function which is defined by a function of it's integral

How can I find $f(x)$ in below relation? $f(x)= e^{I}$ $I = c_1 e^{-x^2/x0^2} - \int_0^\inf (\frac{c_2 (x_2 - x)}{(c_3^2+(x2-x)^2)^{\frac{5}{2}}}+ \frac{c_4(x2-x1)}{(c_3^2+(x2-x1)^2)^{\frac{7}{2}}})...
1
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0answers
98 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, ...
5
votes
1answer
185 views

Numerical Solution of Fredholm Integral Equation Using Bernstein Polynomials

I'm trying to solve a Integral equation: $$y(x)-\int_{-1}^1 \left(x^4-t^4\right) y(t) \, dt=x$$ for n > 5 my code is very slow. How to speed up? Example 2 ...
3
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2answers
129 views

Package for numerically solving Linear Integro Differential equation

Are there any packages or readily available methods for solving linear integro differential equations of the form $\dot{f}(t)=-\int_0^t g(t-s)f(s)\mathrm{d}s$ Thanks already for the answer! Martin
0
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0answers
44 views

Efficiently Plotting NIntegrate with Variable Integration Limit [duplicate]

Consider $g(x)$ which is mathematically defined as $g(x) = \int^{x}_{x_0} f(x') dx'$ such that $x\in\{x_0,x_{max}\}$. If $f(x)$ can only be integrated numerically, one could define the following ...
0
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1answer
88 views

PDE with integral

I am trying to solve PDE containing integral. Its form is showed below: D[Pa[t],t] == Integrate[-k[x]*Pa[t],{x,0,1}] k[x_] := 2*x with initial conditions: ...
0
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1answer
169 views

Triple integral with dependent parameters

The form of my problem is as follows: $\Psi=C\int_{-\infty}^\infty\int_{-\infty}^\infty\left(f(x,y)\times \left(\int_0^t g(x,t)dt\right)dxdy\right)$ I have already attempted numerical solutions ...
8
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2answers
210 views

Is it possible to take a numerical (integral) average of the dependent variable, within NDSolve, at each iteration?

tl;dr: want to integrate (average) the dependent variable within NDSolve. I am currently trying to implement a basic diffusion-advection equation for a reactant, A. The species is converted between A ...
2
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1answer
231 views

How to handle this constant-interval integral in ODE?

The problem is to solve a system of nonlinear integro-differential equation with a Fredholm integral. $Q_i(x), i=1,2,3, x \in [-\text{max},\text{max}]$ \begin{align*} m_i{Q_i}''(x)-V_i(\vec{Q})-d_i\...
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1answer
71 views

Integral equations

Why Mathehtica could not solve the simple equation $$\text{DSolve}\left[-\int_0^x t^4 (t-x)^4 y(t) \, dt-\frac{313 x^4}{15120}+\frac{115 x^2}{252}+\left(\frac{13 x^4}{15120}+\frac{11 x^2}{252}+1\right)...
0
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1answer
99 views

Solve simultaneous integral equations [closed]

I am a beginner at mathematica, so I have made huge blunders in my code which gave too many errors so I did not think it would be relevant to post it. I will try and explain my target as well as ...
0
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1answer
66 views

Why is this integral equation not solved?

In response to this input: DSolve[t[x] == (1/2) Integrate[t[y], {y, x - 1, x + 1}], t[x], x] Mathematica just returns the same input. However, it is easy to see ...
0
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1answer
333 views

Compute the half width and full width at half maximum (HWHM / FWHM) of a mathematical expression

I have managed to compute the half width at half maximum (HWHM) and full width at half maximum (FWHM) of a sinc function through the code below. ...
2
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2answers
145 views

DSolveValue not working

I'm having trouble trying to solve the following volterra (integral) equation with DSolveValue: $$f(x) = \frac{r}{n-1}\left(\frac{1}{\alpha} - 1\right)-\frac{r}{n-1}\frac{(1-p)}{p}e^{n\int\limits_{0}^{...