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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40 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
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2answers
182 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 ...
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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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2answers
304 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
168 views

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

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

How to plot a 2 variable function of an integral?

I have this function: $$E_p(x_0,y_0,t)=E_0e^{-i\omega t}\int^{\frac{a}2}_{\frac{-a}2}\int^{\frac{b}2}_{\frac{-b}2}\frac{e^{ik\sqrt{(x-x_0)^2+(y-y_0)^2+z^2}}}{\sqrt{(x-x_0)^2+(y-y_0)^2+z^2}}dxdy$$ ...
10
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2answers
482 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 ...
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1answer
151 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
339 views

NDSolve Integro-differential equation

I have hard time to solve numerically the following integro-differential equation: ...
2
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1answer
183 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}}-{...
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3answers
179 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 ...
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2answers
339 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)...
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1answer
55 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 ...
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0answers
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 ...
5
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2answers
424 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{\...
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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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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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2answers
237 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 ...
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0answers
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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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 ...
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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}}})...
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0answers
116 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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1answer
217 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 ...
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2answers
145 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
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0answers
51 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 ...
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1answer
96 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: ...
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1answer
231 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 ...
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2answers
287 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
256 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
73 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)...
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1answer
142 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 ...
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1answer
69 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 ...
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1answer
528 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
178 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}^{...
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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1answer
277 views

iteratively solve integral equation

Updated: I am solving the following integral equation for $f(k)$ $$f(k)=-\iint d^2p\,d^2q\frac1{g(p)}\frac1{g(p-q)}\left(\frac 1{g(k-q)}-\frac1{g(-q)}\right)$$ where $g(k)=k^2+f(k)$ so the ...
2
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2answers
1k views

Why won't my integral evaluate?

Not sure why Mathematica won't integrate the definite or indefinite form of my function. I've tried the indefinite integral and it returns unevaluated. How can I see (and evaluate) what the actual ...
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2answers
151 views

Mathematica giving imaginary solutions to an equation having real roots [closed]

Consider the cubic equation : $$ 336 - 1269 t + 1366 t^2 - 360 t^3 == 0 $$ When I use : Solve[336 - 1269 t + 1366 t^2 - 360 t^3 == 0, t] It prints me the ...
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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
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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1answer
109 views

Nested Integrals Using NIntegrate Not Converging

I have a mathematica script/code that I wrote that involves a few nested NIntegrate functions but its not converging. I let it run for about a week before calling it quits. I am a beginner with ...
5
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2answers
2k views

Numerically solve an integro-differential equation

So the problem is to numerically solve this Integro-Differential Equation, $$-v \frac{\:\mathrm{d}\kern0.1mm x(\zeta)}{\:\mathrm{d}\kern0.1mm \zeta} + \psi(\zeta) x(\zeta) + \int_{0}^{\zeta} f(\zeta, \...
0
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1answer
171 views

Numerical solution to an integral equation

I know this question mayn't be new, but here is my problem: I have to solve this integral equation (numerically, of course, except from very few special cases): $$\phi_{\nu}(t) = 1 - q\int_0^t \frac{...
0
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1answer
192 views

How to solve the integro differential equations with matrix

I have integro-differential equations like $X'(t)=\operatorname{diag}(\int_0^t X(t) dt)AX(t)-X(t)$, where $A$ is a known $N\times N$ matrix and $X$ is a $N\times 1$ vector, and $\operatorname{diag}$...
3
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1answer
261 views

exponential differential integral equation

I have a following equation, which has a singular kernel, ...
2
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1answer
142 views

NDSolve cannot solve an ODE system with functions given as integrals-

The problem is that my Mathematica programme cannot solve the differential algebraic equations system. To simplify the problem as much as possible I will consider only the differential equation (which ...
2
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2answers
138 views

Unable to integrate function using Integrate

I'm looking to the result of the following integral: $$\int_0^{\infty} f(g)\exp(-tg) dg $$ where: $f(g) = \frac{ckg^{(c-1)}}{(1+g^c)^{k+1}}$ is a PDF not defined in 0 but with $\int_0^\infty f_G(g) = ...
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1answer
218 views

How to validate the solution of a system of integro-differential equations?

I have successfully solved a system of integro-differential equations. The system is ...