Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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0answers
39 views

Order of evaluation for numeric functions

I'm trying to plot a 3D vector field to illustrate an electric field of a uniformly charged disk, and I used Manipulate to change the radius R of the disk to see ...
0
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0answers
50 views

Integration with a sharp peak

This question is related to my previous question: Avoid Evaluation of Function at NDSolve I have a function which behaves like in the following figures: These graphs are cuts from an interval. My ...
0
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2answers
60 views

NIntegrate problem with limits in triple integral [closed]

So I am trying to solve a triple integral in mathematica, but I am getting errors regarding my limits of integration. This is my code: ...
1
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1answer
340 views

How to code the following in Mathematica

How do I get the following into Mathematica, solving for a: $$ 0.7 = 1 - \frac{2}{a} \times [ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1} dx + \frac{a}{6} - 1] $$
0
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0answers
48 views

Time needed to solve NIntegrate is much longer than what I was expecting

I'm trying to do the following list: tablevdip = ParallelTable[{x, y, Vdip[x, y, 6]}, {x, -1, 1, .5}, {y, -1, 1, .5}];] with ...
3
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0answers
56 views

Avoid Evaluation of Function at NDSolve

I have a huge "black-box" f function, which I want to integrate. Let's define it: f[x_,y_,a_]:=a*Exp[-(a*10000)(x^3+y^3)] as ...
0
votes
1answer
73 views

Integrating high oscillatory function - triple integral - error message

I am working in a triple integral, but the second integral (qQ) and the first too ( aA ) is a oscillatory funcion. The third integral ( os11 ) is like a gaussian, and is easy to integrate. i am ...
2
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2answers
102 views

Solving nonlinear 3rd order ODE over range from zero to infinity

Here are the code that I had tried but there is an error ...
0
votes
1answer
164 views

Plotting singular integral

I need to plot the following singular double integration $u(x,t)$ for $t=0, t=0.2, t=0.4, t=1$ and $t=2$ in one figure as a line. That is, I need $u$-coordinate vertically and $x$-coordinate ...
1
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1answer
42 views

Nested NIntegrate with variables in limits

How do I solve nummerically something like this and plot a function for it? $f(x)=\int \exp[\int ^{x+y} _{x-y} \exp(z) dz]dy $ This example has analytical solution, however I would like to know how ...
4
votes
1answer
61 views

WorkingPrecision and NDSolve Method Plugin Framework

I'm studying some new numerical integration algorithms using NDSolve Method Framework to specify them. When I try to set ...
2
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0answers
55 views

WhenEvent behavior changed from v9 to v10 - how to fix the code?

A couple of years ago I asked a question about solving n-body systems with NDSolve and detecting collisions with WhenEvent. I ...
2
votes
2answers
74 views

Function where variable is integration bound

Lets say I have a function of the form: $f(T) = T^4 \int_0^{1/T} \frac{x^3 dx}{e^x-1}$ This is an example of the situation I am describing not a unique problem. I want to define it as a numerical ...
6
votes
3answers
187 views

Certain integral over torus

Let $F(t_1,s_1,t_2,s_2)=$ $$\big((2+\cos t_1)\cos s_1 - (2+\cos t_2)\cos s_2\big)^2 + \big((2+\cos t_1)\sin s_1-(2+\cos t_2)\sin s_2\big)^2 + (\sin t_1 -\sin t_2 )^2.$$ I am interested in computing ...
1
vote
1answer
131 views

How do I plot this 3-D, double integral?

I have the following function: I need to plot a 3-D with coordinates f (p, q), p and q. I mean, I enter values for p and q, so that the integral of f (p, q) must be a number. This number must be ...
11
votes
1answer
227 views

How can I use Mathematica to numerically compute a Wigner spectrogram of an optical pulse?

This question was inspired by this question where it is necessary to numerically compute the Fourier transform of a Gaussian optical pulse with a Gaussian chirp function. $$E(t)=e^{-t^2} \cos(50 t - ...
0
votes
1answer
128 views

NDSolve breaking down

I'm trying to model a situation involving charged sphere in a dynamic electric potential, and find out how the rotational motion of the sphere affects the translational dynamics in two dimensions. ...
3
votes
1answer
70 views

Numerical integration with parameter and plot

I'm working on this function: (0.0027 Sin[phi])/(1.05*Exp[-241w]+ Exp[239w]-Cos[phi]) I'd want NIntegrate this function on ...
3
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1answer
52 views

How can I plot points generated by a Verlet Integration?

So, I have this code for Verlet Integration: ...
2
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0answers
47 views

Discretised numerical solution to a non-linear non-local equation

I understand that to do something even slightly non-trivial in Mathematica, I need to read some materials; the problem is that there are (too) many materials and only one particular problem, and I ...
3
votes
2answers
186 views

Error in NIntegrate command

I am trying to evaluate (numerically) the integral $$\int_0^1\int_0^1\int_0^1\int_0^1\int_0^1\int_0^1\frac{dx\,dy\,dz\,ds\,dt\,du}{(x - s)^2 + (y - t)^2 + (z - u)^2}$$ with Mathematica using the ...
6
votes
2answers
222 views

Solving the path of Earth around Sun

This maybe isn't a universally helpful question. Maybe a little of a code dump. But here goes. I'm trying to solve the path Earth moves around Sun from Earths mass, Suns mass, Earths initial velocity ...
1
vote
1answer
74 views

Nonlinear 2nd order ODE with regular singularities

I am tring to solve the following ODE with NDsolve $2x~(1-x)~f''(x)+(3-4x)~f'(x)+a~f(x)+b~f^n(x)=0;~~a,b\in\mathbb{R},~n\in\mathbb{N}$. The mathematica "code" is: ...
1
vote
1answer
361 views

Numerical solution of Schrödinger equation

I want to solve the following differential equation numerically. The geometry of the problem is as shown below. Electron 1 is located on the inner ring of radius $R_1$ and electron 2 is located on the ...
1
vote
1answer
47 views
15
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2answers
255 views

More efficient method to compute moments of the Johnson $S_B$ distribution

Here is a very specific feature request. I need Mean[JohnsonDistribution["SB", γ, δ, 0, 1]] When I issue e.g. ...
2
votes
0answers
114 views

How to solve an equation where the unknown variable is inside the integration [closed]

I have an equation: $$ \frac{1}{g}=\int_0^{\frac{1}{\delta}\sinh \frac{1}{g}} \frac{\tanh\left(0.882\, b\,\delta\sqrt{1+z^2}\right)}{\sqrt{1+z^2}}\mathrm{d}z $$ I want to obtain the relation ...
1
vote
1answer
63 views

Convergence in NIntegrate

I wish to understand how to cope with the following error messages: ...
0
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0answers
68 views

How to solve boundary value problem with singularities at boundaries?

I have a boundary value problem, solving a system of differential equations with a singular boundary condtion (V[0] = 1/s, s->0) ...
0
votes
0answers
68 views

Plotting multiple numerical integrations

I have the following query regarding plotting a numerical integration for which the code is given below ...
2
votes
0answers
59 views

NIntegrate over statistical variables with parameter

Essentially, what I am trying to do is the following: Integrate a function which contains the parameter k ...
0
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1answer
67 views

NIntegrate with variable limit of integration [duplicate]

Hey guys Im working with this integral and I can´t get it right. ...
-1
votes
1answer
261 views

Follow up: how to plot a function under NDSolve domain

Here is the details of the code to plot. ...
1
vote
0answers
101 views

integration of a list of gaussian type orbitals (GTO)

I am currently trying to integrate various components of a current density (j={jx,jy,jz}) over space. The problem is that the current j is extracted from a quantum chemical computation and is a sum of ...
0
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2answers
69 views

Fit a polynomial/curve to an NIntegrate result

I want to NIntegrate a function which also contains some parameter. In the end, I would like to plot the result as a function of one of these parameters. The thing ...
2
votes
2answers
195 views

Attempting to use NDSolve to plot harmonic oscillator solutions

NDSolve[{ (-y''[r]/1880) + (470 (0.04077)^2 r^2 - 48 + 1/(1880 r^2)) y[r] == 0, y[0] = 0, y'[0] = 0}, y, {r, -4, 4}] I use this but get errors and am ...
5
votes
1answer
119 views

A 1D numerical integral Mathematica cannot compute, from physics

A well know result in theoretical physics is that a sum over Matsubara fermionic frequencies, i.e.: $$ S = \sum_{n=-\infty}^{\infty} h(\omega_n) \hspace{32pt} \omega_n=(2n+1)\frac{\pi}{\beta} $$ can ...
1
vote
2answers
102 views

Trapezoid Integration over a list of pairs [duplicate]

I have two very connected questions: Is there really no built-in function to integrate a list of pairs without converting to a function? Something like: ...
0
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2answers
174 views

Solving non-linear differential equation

For my research project I need to solve the following integral ...
1
vote
1answer
93 views

Problem with NIntegrate and FindFit [closed]

I fit the experimental curve with the model using the following equation, ...
1
vote
0answers
45 views

Problem with curve fit using integral [closed]

I need fitting a Langevin function on a experimental data, but one parameter must be firstly optimized by using a Lognormal distribution. The complete expression could be written as: The integrate ...
7
votes
2answers
188 views

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
1
vote
2answers
85 views

Can't NIntegrate my NDSolve results

I want to NIntegrate my NDSolve result. I don't have a exact function form because it is coming from the ...
2
votes
1answer
53 views

WhenEvent stops working after first instance

I'm modelling a very simple physical situation is which an object is rested on two moving fingers. Sometimes the object moves with one finger while sliding over the other, while at other critical ...
0
votes
0answers
42 views

NIntegrate within NMinimize - how to optimize the code?

How I can optimize these numerical calculations? Most annoying is encountering instabilities (numerical errors). I have a predefined function: ...
3
votes
2answers
105 views

Numerical integration of oscillatory function

I am trying to evaluate the following oscillatory integration numerically but the answers are wrong or not accurate enough. I don't know what the problem is. ...
7
votes
2answers
210 views

NIntegrate fails to converge under almost any PrecisionGoal, MinRecursion etc. How can I trust the result?

I have been getting some ideas by reading other related questions in the forum, but the integral I have to do is not converging in many cases. The integrand is of the form: ...
2
votes
2answers
87 views

numerical integration of equation obtained by ParametricNDSolve

I am trying to find a definite integral of the solution obtained using ParametricNDSolve (i.e. y[x,a,b]) from 0 to 1 and plot ...
15
votes
1answer
1k views

Numerical integration — Mathematica vs Python (w/ Scipy) performance

I'm about to tackle a problem that involves a lot of (multi-dimensional) numerical integrations and also subsequent optimizations, and so I want to make sure at least the integration step is as fast ...
1
vote
0answers
56 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...