All Questions
Tagged with calculus-and-analysis numerical-integration
611 questions
8
votes
2
answers
418
views
NIntegrate cannot give high precision result for a well-behaved integral
I want to obtain value of following integral to a high precision (say 30 digits),
NIntegrate[DawsonF[Sqrt[t]]^2/t, {t, 0, Infinity}]
Graph of integrand looks like ...
- 311
5
votes
3
answers
332
views
NIntegrate doesn't calculate a triple integral
I have an integral of dubious origin, which I don't know how to calculate:
...
- 387
-1
votes
1
answer
52
views
Extend of numerical ODE for a special case [duplicate]
I want to continue the plot but I don't know how to do it?
...
- 465
0
votes
1
answer
62
views
Compute integrals in singular integral equation
I'm looking at this paper
https://arxiv.org/abs/2404.07307
and in particular I am interested in eqs. (16) (17), meaning I'd like to check the validity of (16) by insert it in (17).
So I'd like to ...
- 31
1
vote
0
answers
116
views
Integrate numerically over implicit complex contour
I'm trying to numerically evaluate the following integral:
$$
\int_0^\infty dt\ e^{-(a+i\alpha) t}(1+e^{-t})^{-(b+i\beta)},
$$
where $a,b$ are some rational numbers and $\alpha,\beta$ are relatively ...
- 269
4
votes
3
answers
212
views
Solving integral equation numerically
I tried to solve a integral equation numerically, but I failed. The equation is:$\epsilon(\beta)=r\cosh{\beta}+\int^{\infty}_{-\infty}\varphi(\beta-\beta')\ln(1+e^{-\epsilon(\beta')})d\beta'$ were $\...
5
votes
0
answers
171
views
Hypergeometric Function Integration Using Mellin-Barnes Representation
I have the following integral:
$$
I=\int_0^1 d \alpha d \beta d \gamma r(\gamma) s(\alpha, \beta) T(\alpha, \beta, \gamma)
$$
where I define
$$r(\gamma)=(\gamma(1-\gamma))^{ -1 / 2+\epsilon / 2}$$
and,...
- 139
0
votes
0
answers
49
views
NDSolve for non-linear Poisson equation: the case of a pn diode
I am solving the physical problem of a pn diode under no bias voltage. This involves solving a rather 'complicated' non-linear Poisson's equation in 1D
\begin{equation}
-\frac{\partial^2\phi(z)}{\...
- 585
-3
votes
1
answer
128
views
I have a error on my code but I can't find it!
I have a problem by my code I can't find it yet!!
...
- 465
1
vote
1
answer
129
views
2-loop diagrams dimensional regularization with Feyncalc
I attempted to evaluate the following diagram using FeynCalc, following the method outlined by Pierre Ramond in his QFT book, but I encountered difficulties:
\begin{equation}
\Sigma(p)=\frac{\lambda^2\...
- 139
0
votes
0
answers
39
views
Integration or numerical integration over one variable out of many variables
I have a function defined as
AFB = (6*I6parSMM)/(2*(3*I1cparSMM + 6*I1sparSMM - I2cparSMM - 2*I2sparSMM));
where the I'parSMM's are functions of other variables s, ...
- 111
3
votes
1
answer
102
views
Many contradictory results for a single integral
I am interested in solving the integral $$
\int_{\mathbb{R}} dx \frac{e^{i a x^2}}{(x - b - ic)^d(x - b + ic)^d}
$$
for $a,b,c \in \mathbb{R}$ and $d \in \mathbb{N}$. As an early step, I have asked ...
- 131
4
votes
3
answers
294
views
How is the result of this integral obtained by the function `Integrate`?
When I use Mathematica to calculate
$$
\int_0^{+\infty } \frac{\log (1-\mathrm i x)}{1+x^2} \, \mathrm dx ,
$$
I get different results using functions NIntegrate ...
- 433
2
votes
2
answers
103
views
Partial Derivative after Numerical Integration of a Complicated Expression with Singularity at Zero
I want to generate Fig no. 2,3,4 from https://arxiv.org/pdf/2212.08237
with the help of the following equations. In Fig 3 t_(opt) is the time Q_T reaches its max value Q_T(opt) for each T.
Here is ...
- 297
9
votes
8
answers
773
views
Numerical approximation of the integral by using data
I want to use the numerical approximation of the integral of a function given a list of data:
$$\int_a^bf(x)dx\approx\sum_{k=1}^N\frac{f(x_{k})+f(x_{k-1})}{2}(x_{k}-x_{k-1}),$$
where $f(x_0)=f(a)$ and ...
- 685
1
vote
2
answers
140
views
Solution of an implicit integral equation
The present question is pretty similar to this one.
Here I want to find the solution of the following implicit integral equation:
$$
P_H(u)=\int_{-\infty}^\infty dJ \int_{-\infty}^\infty du_1 \int_{-\...
- 405
0
votes
1
answer
146
views
NIntegrate can't solve this complicated multiple integration with absolute value in Exp and Cos functions
I'm trying to use NIntegrate to calculate this complicated multiple integration, which has absolute value in the Exp and Cos functions.
$$
\int_{-\infty}^{\infty} dx_1 \int_{-\infty}^{\infty} dx_2 \...
- 1
1
vote
1
answer
58
views
Errors in `NIntegrate` - or in coding?
As far as I know, if a set of functions f,g,h,... are all Riemann integrable then the definite integral of the sum f+g+h over ...
- 2,335
0
votes
1
answer
94
views
Vortex beam profile plot [duplicate]
I want to plot this type of plot for the Lagurree Gaussian beam
$\begin{aligned} u(r, \phi, z)= & C_{l p}^{L G} \frac{w_0}{w(z)}\left(\frac{r \sqrt{2}}{w(z)}\right)^{|l|} \exp \left(-\frac{r^2}{w^...
0
votes
0
answers
50
views
NIntegrate with depended variables
I have problems in integrating a function with depended variables. I am pasting the code below
...
1
vote
1
answer
161
views
Find the polar plane of the ellipsoid and integrate the Ellipsoid cap
I am working on writing a code to find the polar plane of an ellipse, and subsequently calculate the cap formed by subtending the point $p$ (red) onto a random ellipse.
I think I have managed to ...
- 633
2
votes
2
answers
279
views
How to calculate a definite integral with a parameter
I am trying to calculate the following definite integral with the parameter H. So my result would like to be a analytical one with the parameter H. For example for the integral NIntegrate[ax, {x, 1, ...
2
votes
1
answer
83
views
Generate variables in multiple integral
I want to do a multiple integrate with n variables. When I change the value of n, I do not want to rewrite the variables in the integral manually like here:
...
- 185
3
votes
1
answer
71
views
Integral of interpolation function is not evaluated
I am having a misunderstanding with Mathematica about integration of InterpolatingFunction. Consider this example:
...
- 4,036
0
votes
2
answers
73
views
Comparing Closed-form to Numerical Integral Result
When I numerically calculate this integral
NIntegrate[(1/2)*Log[1 + Sin[x]]^2, {x, 0, Pi}]
The result is $0.416217488896557$ and I verified it using another tool....
- 3,464
3
votes
1
answer
119
views
Asymptotic integral expansion at infinity [closed]
Define for all $n\in\mathbb{N}$, a definite double integral, $$I_n= \int_{0}^{1}\int_{0}^{1}\left(\frac{x^2(1-x)y^2(1-y)}{1+x^2 y^2}\right)^n\frac{\cos((2n+1)\tan^{-1}(xy))}{\sqrt{1+x^2y^2}}\ dxdy$$
...
- 301
2
votes
1
answer
42
views
Nested NIntegrate with limit variable dependance
Hope you are doing great!
I am trying to solve a double Integral of a function let's say f(w,q).
My upper and lower limits are
...
1
vote
1
answer
38
views
Not able to integrate function involving scalar product
For given $h=0.2,D=1.5$, let $w_{i}(x):=\frac{1}{\pi D}\exp^{-||\frac{x-hi}{\sqrt{D}h}||^{2}}$ where $x\in \mathbb{R}^{2}$ and $i\in I \subset \mathbb{Z}^{2}.$ For $x\in \mathbb{R}^{2}$ ,let $v(x):=-...
- 15
8
votes
2
answers
200
views
Numerical integral does not agree with analytic integral
I am trying to evaluate a function, that I've now reduced to its minimum (not) working example. Unless I am doing something very wrong, it appears that NIntegrate ...
- 97
0
votes
0
answers
150
views
Unable to compute integral on implicit region
I am new to Mathematica. I need to deal with the following computation
...
- 101
4
votes
1
answer
118
views
Numerical Solution for a Non-Linear Functional Fractional Differential Equation (FFDE)
I tried solve non-linear Functional-Fractional Differential Equation (FFDE) with this method, but it works on only for range: $x\in \{0,1\}$.
I what extend the solution range for example for general ...
- 16.6k
3
votes
1
answer
118
views
Strange analytical and numerical results during an integration of a complex integrand
Mma 13.2.1.0 Win 10 Pro
I am solving the following integral:
...
- 40k
3
votes
1
answer
150
views
Numeric integration and RegionDilation in higher dimensions
I would like to integrate over a dilationed region in higher dimensions.
In 3 dimensions it works well.
...
- 185
1
vote
2
answers
151
views
Is there any hope that Mathematica answers this parametric integral? [closed]
Is there any hope that Mathematica answers this integral?
Integrate[ Exp[a (b/(c + 2 (1 + x) d)^4 - (e + f/(c + 2 (1 + x) d)^2)^2/(
4 (2 + x + g)^2))], x]
...
- 749
3
votes
2
answers
173
views
Disagreement between symbolic and numerical integration
I am trying to get the integral of a rather complicated function:
$$
\int_{t_1}^{t_2}m_{\text{basal}}+m_{\text{size}}\exp\left(\frac{1}{2}\left(\ln(S_{t_1})+\frac{u-t_1}{t_2-t_1}(\ln(S_{t_2})-\ln(S_{...
1
vote
0
answers
35
views
How to NIntegrate the result of NDSolveValue over the IVs?
I want to integrate functional g of the solution of f over the IVs.
...
- 215
-1
votes
1
answer
122
views
Expression for an integral
I am facing a problem obtaining an expression for my integral. My code goes in a time-consuming loop whenever I execute this integral. The code is:
...
- 119
3
votes
1
answer
239
views
Numerical computation of magnetic Euler-Heisenberg integral
The Euler-Heisenberg action describes non-linear interactions of electromagnetic fields. The case I am interested in corresponds to the ideal MHD limit (with vanishing electric field), where the ...
0
votes
1
answer
53
views
Trouble using Integrate as the model in NonlinearModelFit
I'm trying to fit a set of heat capacity data to the Debye model.
This is the sample dataset that I'm using:
...
0
votes
1
answer
52
views
Plotting an integral with solving for a specific constant [closed]
Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
- 117
1
vote
1
answer
107
views
Plot after applying NIntegrate
I'm trying to integrate and graph $I$ vs $b$ the following integral (eq. 24 in this paper) in wolfram mathematica
$$ I = \int_{2}^{\infty} \frac{g_i^3 \mathcal{K}_t \mathrm{~d} r}{r^2\left|\mathcal{K}...
- 117
0
votes
1
answer
107
views
Change of variable of a numerically solved integral
I have the following function that numerically integrates a function on the interval $\left[ 2, 100 \right]$
...
- 117
1
vote
0
answers
88
views
Intensity pattern [closed]
I'm trying to get the following intensity pattern from this paper
In the Newtonian case, the equations for the intensity (eq. 9 and 10 in the article), I put them in Mathematica with the change $b^2 =...
- 117
0
votes
2
answers
99
views
How to chose appropriate finite limits for NIntegrate?
I want to NIntegrate a function using finite limits so it gives a result as close as possible to a result which I would get making the limit ...
- 55
1
vote
1
answer
273
views
Plot solution of an integral with parameter
In this article, they solve the following integral
$$ \mathcal{I}_{o b s}\left(\nu_0\right)=\int_{\gamma_i} \frac{(A(r))^{3 / 2}}{r^2} \sqrt{\frac{1}{A(r)}+r^2\left(\frac{d \varphi}{d r}\right)^2} d r ...
- 117
5
votes
1
answer
237
views
Implementation of SINC filter using Integrate results in incorrect output
Bug introduced in 6.0, persisting through 13.3.1.
This is SINC filter, integrate $|H|^2$ from $-\pi/2$ to $\pi/2$.
MMA CODE, Result = 7.27956e-12
...
- 147
0
votes
1
answer
53
views
Different integral values for analytically same integrals
Consider a function $L$ with parameters $h=0.1,\ D=1.5$
$L(m,x):=e^{-\frac{2\ (\frac{x}{h}-m)^{2}}{D}}$.
While the integrals $\int_{-\infty}^{+\infty}L(0,x)dx$ and $\int_{-\infty}^{+\infty}L(40,x)dx$ ...
- 15
1
vote
3
answers
216
views
Integration giving unknown messages
I am trying to integrate the following
Integrate[(Log[1 - t] t^(-(1/2) + eps))/(1 + t),{t,0,1}]
To simplify this I am doing a further transformation ...
- 1,907
3
votes
1
answer
168
views
Accuracy of numerical solutions provided by pdetoode
I am interested in solving the following differential equation using pdetoode
(you can find pdetoode here).
...
- 597
3
votes
4
answers
334
views
Volume of Region Contained by 3D Data Points
I have a dataset consisting of (x,y,z) data that describe a surface, and I need to find the volume of the region bounded by that surface. The data do not follow any mathematical equation, but the ...
- 85