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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.

2
votes
1answer
169 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
vote
1answer
55 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
votes
0answers
57 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 ...
1
vote
1answer
188 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
votes
1answer
37 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
votes
2answers
172 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
vote
0answers
89 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
votes
2answers
238 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
votes
1answer
130 views

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

I do not know how to handle the integro-term. ...
5
votes
1answer
316 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
vote
1answer
35 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
votes
2answers
261 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
votes
1answer
58 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 ...
1
vote
3answers
165 views

NDSolve Integro-differential equation

I have hard time to solve numerically the following integro-differential equation: ...
2
votes
1answer
151 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
vote
3answers
116 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
votes
2answers
246 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
vote
1answer
45 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
vote
0answers
74 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
votes
2answers
215 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
votes
0answers
121 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
votes
0answers
58 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
votes
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
votes
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
vote
0answers
73 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
votes
0answers
93 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
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
vote
0answers
95 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
178 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
votes
2answers
127 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
votes
0answers
43 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
votes
1answer
84 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
votes
1answer
146 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
votes
2answers
202 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
votes
1answer
225 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\...
1
vote
1answer
69 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
votes
1answer
94 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
votes
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
votes
1answer
285 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
votes
2answers
134 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
votes
0answers
237 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
1answer
161 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
votes
2answers
526 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 ...
0
votes
2answers
108 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 ...
1
vote
0answers
127 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: ...
0
votes
0answers
40 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
1answer
87 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 ...
4
votes
2answers
947 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
votes
1answer
143 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{...