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.

Filter by
Sorted by
Tagged with
1
vote
2answers
100 views

Solving integro-differential equation [closed]

I would like to solve the integro-differential equation of the form $$\left( -n \int_0^b b db + \frac{i \Lambda l_P^2}{9V_c}\frac{d}{db}+b^2+k\right)\psi(b)=0.$$ I followed the steps in Solve an ...
0
votes
1answer
33 views

Problem plotting expression involving Generalized hypergeometric functions $_2F_2 \left(.,.,. \right)$

I'm trying to plot a graph for the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]=a 2^{-\frac{\kappa }{2}-1} b^{-\frac{\kappa }{2}} \theta ^{-\kappa } \...
11
votes
1answer
138 views

High precision numerical solution of the nonlinear Volterra integral equation

Let consider nonlinear Volterra integral equation 5.1 from the paper An iterative multistep kernel based method for nonlinear Volterra integral and integro-differential equations of fractional order $$...
2
votes
1answer
68 views

Getting two different results for the same computation

I have the following two codes: ...
2
votes
1answer
83 views

How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
2
votes
1answer
114 views

Integral of $r \frac{2^{r-1} \log (2) e^{-\frac{\sqrt{2^r-1}}{b}} \left(2^r-1\right)^{\frac{d}{2}-1}}{b^d \Gamma (d)}$ with Mathematica

I'm trying to find the integral given below with Mathematica $\int_0^{\infty } r \frac{2^{r-1} \log (2) e^{-\frac{\sqrt{2^r-1}}{b}} \left(2^r-1\right)^{\frac{d}{2}-1}}{b^d \Gamma (d)} \, dr$ However, ...
0
votes
1answer
38 views

Gaussian Integral incorrect

I'm trying to learn about the Gaussian Normal distribution using Mathematica. So I defined my Gaussian like this ...
3
votes
0answers
60 views

Why this change gives different results in Integrate?

I'm new in Mathematica and can't understand why changing a number from Real to Integer is giving different results in my equations: ...
0
votes
1answer
50 views

Definite integral Closed-form or approximation\simplication or a plot diagram shows the variation based on $a$ and $b$

I am not professional in Mathematica and I am struggling to understand how the following function acts $f(x)=\int_{z=0}^\infty \int_{y=0}^{z} \frac{x}{ \sqrt{1-\left(\frac{z^2+y^2-x^2}{2 z y}\right)^2}...
1
vote
1answer
51 views

Integrating Superposition of several sinusoidal waves squared times its derivative

I'm currently finishing some research from a internship I did last summer and part of the project involves calculating the centroids of coronal holes from synoptic maps. If you aren't aware of what ...
-4
votes
1answer
163 views

Solving some integral equations [closed]

I couldn't solve the systems, I need plot graph of solution: ...
5
votes
1answer
146 views

Numerically solving a multivariable integro-differential equation

I have an integro-differential equation of the form, $$\small\frac{\partial f(x,t)}{\partial t}=\int_{-5}^5 |x-y|\,f\left(-\frac{x}{3}+\frac{4y}{3},t\right)\,f\left(\frac{2x}{3}+\frac{y}{3},t\right)\,...
3
votes
2answers
216 views

How to solve this integral equation using Mathematica?

My question: How do I use Mathematica to find the solution to Case 2? As a cross check for the code, does it verify the solution in Case I? Case 1: We will look at an easier problem first. Let $|\...
0
votes
1answer
49 views

How should one evaluate this integral [closed]

How does one go about evaluating such an integral where E and V are constants? $\int\sqrt{E-Vx^8}dx$
0
votes
1answer
50 views

How to 3DPlot a triple integral in cartesian coordinates

I am trying to make a 3d graph of the triple integral in cartesian coordinates. I am positive that I have been filling out the correct parameters but I am unsure what could be wrong. Additionally I ...
9
votes
2answers
350 views

Testing Turbulence Models

In the 90s, several turbulence models were proposed. Using Mathematica vv 10-12.1 we tested two models: 1) Spalart-Allmaras turbulence model (SA) for aerodynamic applications, published in AIAA ...
2
votes
1answer
121 views

How do I plot a definite integral on Mathematica?

I am not sure how to put this in good format, but I want to plot this on Mathematica: $$ u(t) = \frac{1}{4\pi t} \int\mathrm dy\ \mathrm e^{-y^2/(4t)}\ y\ (1 - y^2) $$ on the interval $ [a, b] $ ...
1
vote
1answer
97 views

How can I always get the simplest solution from Integrate? [closed]

When I evaluate this. Integrate[1/(x (1 + x^4)^(1/4)), x] // FullSimplify In 11.3 I get ...
0
votes
1answer
175 views

How to calculate integration with undefined functions?

There are two functions inside the integral symbol, one is related to the independent variable and the other is independent of the independent variable. Both are the derivative and Tload is a ...
2
votes
0answers
45 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 ...
1
vote
0answers
135 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 -...
0
votes
1answer
95 views

Double integration of an exponential function which includes a Csch function and complex numbers

Mathematica couldn't solve following using just integrate function. I checked on interpolating as well, that also turned to be a dead end. Can someone help me with evaluating this integral? If it ...
1
vote
0answers
55 views

How solve integral with three moment and delta function [closed]

I am trying solve this integral in mathematica: \begin{equation} \int \dfrac{d^3 p_3}{(2\pi)^3 2 E_3} \dfrac{d^3 p_4}{(2\pi)^3 2 E_4}(p_1 p_2)(p_3 p_4) \delta (p_3 + p_4 - p_1 - p_2). \end{equation} ...
3
votes
1answer
184 views

Solving partial integro-differential equation

I want to solve a partial integro-differential equation of this form: using NDSolve, something like ...
3
votes
1answer
226 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
0
votes
1answer
39 views

FindRoot: equation with integral on parametric domain

Writing: ...
1
vote
1answer
79 views

Solve an Integral-differential equation with DSolve

I do not understand why the following code does not solve the equation: ...
1
vote
0answers
40 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 ...
5
votes
1answer
73 views
0
votes
0answers
33 views

Help with NIntegrate with singularity and variable integration limit

I have a function of the type: $$ F(x,z)= \int_{-\infty}^{\infty} dx' \int^{z}_{-\infty} dz' f(z,z',x,x')\frac{\partial g(z',x')}{\partial z'}$$ where the integration order may be interchanged. I ...
-1
votes
1answer
65 views

Definite Integral [closed]

I am not able to do the following integration. \begin{equation} \int_{0}^{a} x\sin^2 \left(\frac{n \pi x}{a} \right)dx \end{equation} It shows an error that "more input is needed". The mathematica ...
1
vote
2answers
124 views

Can't solve for y in a fairly simple work done by magnetic field equation

The equations below are essentially calculations for a railgun-type mechanism (here is a good image description). I also drew an image using my own variables as definitions: I assumed that ...
2
votes
2answers
134 views

Trouble second-order ordinary differential equations with integral terms

I am a beginner of mma. During the learning of differential equations, I encountered a very difficult problem, a second-order system of ordinary differential equations with integral terms. This ...
0
votes
2answers
91 views

Problem with FindRoot function

I have set up a code to solve simultaneous integral equations. These result essentially from taking integrals of the Fermi-Dirac distribution. Although there are no obvious problems with the code it ...
1
vote
1answer
127 views

Regression to fit data with an integral equation

I have a set data and I know that this data are best fitted by the following equation, assuming that f($\tau$) is a log normal distribution and $M_{eq}$ = 1.5: $M(t,\tau)= M_{eq} \int (1-e^{-t/\tau}) ...
1
vote
1answer
143 views

Solving IDE system using FDM based on NDSolve`FiniteDifferenceDerivative

I wanted to solve the following system of integro-differential equations (IDEs) using finite difference method (FDM). $y_1''(t)+t^2y_1(t)-y_2''(t)+\int\limits_0^t[(t-x)y_1(x)+y_2(x)]\mathrm{d}x=(2+t^...
0
votes
2answers
183 views

solve the iterative integral equatio [duplicate]

The following code is incorrect, please specify my mistakes ...
0
votes
1answer
71 views

Solve integral equation by iteration

For[{n = 1, y[0][x_] = 1}, n < 4, n++, y[n][x_] = 1 + Integrate[y[n - 1][t]^2 + t^2, {t, 0, x}]; Print[{n, y[n][t]}]] here how can I get table of values ...
0
votes
2answers
54 views

problem with constant variables

Variable x is supposed to be constant, but the program calculates for each variable x, 100 numbers of x. I want all my x variables to have the same definition, but the program constantly changes each ...
2
votes
2answers
112 views

Unexpected limit result (was: How to fix the limit problem?)

MATHEMATICA fails in proving that Limit[ Integrate[ x^(x - 1) , {x, t, 2*t} ] , t -> 0 , Direction -> "FromAbove" ] == Log[2] How to fix ...
4
votes
1answer
283 views

How to speed up the integral in NDSolve?

On the MMA.SE, there have been several question on how to solve equations including integral using NDSolve, see example 1, example 2, and example 3. Many people, ...
0
votes
0answers
95 views

How to integrate this expression one time? [duplicate]

How can I integrate this expression? I want to have the second derivative of V i.e. V''[r]. Note that, you can multiply it be ...
0
votes
1answer
207 views

How can I create loop for this iteration integration [closed]

I have definite integral of the form $$f(x)=\int_{-\pi}^\pi\frac{x^2-1}{(x^2-1)^2+x^2+y^2+f(x)}dxdy$$ I want to make a code to calculate $f(x)$ numerically, starting from $f(x)=0$ and stopping when ...
3
votes
4answers
503 views

How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$?

How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$ ? Limit[Integrate[(1 - x/n)^n/E^x, {x, 0, n}], n -> Infinity] ...
0
votes
1answer
53 views

Convolve doesn't yeild expected answer, nor does integrate

I am convolving, or trying to, a Gaussian and a Lorentzian as follows: ...
5
votes
1answer
225 views

Solving partial differential equation involving Hilbert transform

While solving one research paper published in Physical Review Letters, I came across the following equation and I am unable to solve it. $$\frac{\partial f}{\partial t}−(\mathcal{H}(f)\left(\frac{\...
1
vote
1answer
61 views

Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
4
votes
2answers
359 views

Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
0
votes
1answer
116 views

Delayed differential equation with convolution

So I have a differential equation : $\left\{\begin{split} & c'(t) = \alpha q(t) c(t)^{2/3} - \beta(1 - q(t))c(t)\\ &\chi'(t) = \kappa c(t) q(t) \\ & q(t) = \int_{-\infty}^t \Big( ...

1
2 3 4 5