Questions on the use of numerical functions NIntegrate and NDSolve.

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0
votes
1answer
135 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. ...
9
votes
4answers
599 views

Calculating an integral by the Romberg Algorithm

In my "Numerical Analysis" course, I learned the Romberg Algorithm to numerically calculate the integral. The Romberg Algorithm as shown below: ...
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
votes
1answer
59 views
3
votes
2answers
195 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 ...
2
votes
0answers
53 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 ...
1
vote
2answers
107 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
0answers
109 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 ...
1
vote
1answer
390 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 ...
6
votes
2answers
263 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
78 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: ...
3
votes
4answers
261 views

NIntegrate Trapezoid rule with even subdivision producing poor results

NIntegrate[x^2, {x, 5, 9}, Method -> {"TrapezoidalRule", "Points" -> 2, "RombergQuadrature" -> False}, MaxRecursion -> 1] returns the ...
10
votes
1answer
1k views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
16
votes
2answers
276 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
133 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
82 views

Convergence in NIntegrate

I wish to understand how to cope with the following error messages: ...
2
votes
2answers
229 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 ...
0
votes
0answers
84 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) ...
6
votes
1answer
689 views
8
votes
1answer
894 views

The difference between “SymbolicProcessing” -> 0 and restricting the function definition to numeric values only

The Documentation tells us that there are two ways to disable symbolic processing of the integrand by the NIntegrate function when it is known that it just slows ...
2
votes
0answers
61 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
votes
1answer
134 views

NIntegrate with variable limit of integration [duplicate]

Hey guys Im working with this integral and I can´t get it right. ...
14
votes
6answers
2k views

How do I obtain the enclosed area of this particular parametric plot?

I'm trying to find a way to obtain the enclosed area of this particular plot. Can someone show me how? ...
0
votes
2answers
330 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
6
votes
2answers
203 views

Why does Nintegrate keep unevaluated?

Bug introduced in 10.0 and fixed in 10.2.0 It's no surprise that the "MonteCarlo" Method works well: ...
2
votes
1answer
294 views

Integrating over a region without singularity gives an error indicating the function has singularity in that region

Bug introduced in 8.0.0 or earlier and fixed in 8.0.4 I have the following 2D region over which I want to integrate a function: ...
0
votes
2answers
75 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 ...
5
votes
1answer
128 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 ...
0
votes
2answers
181 views
1
vote
2answers
129 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: ...
1
vote
1answer
98 views

Problem with NIntegrate and FindFit [closed]

I fit the experimental curve with the model using the following equation, ...
16
votes
3answers
868 views

Only final result from NDSolve

Finally, I started to play with differential equations in Mathematica. And I have faced the problem, which seems to me so basic that I'm afraid this question is going to be closed soon. However, ...
1
vote
0answers
48 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 ...
5
votes
3answers
126 views

Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
5
votes
4answers
246 views

error with NIntegrate and RegionPlot

Bug introduced in 10.2 or earlier and persisting through 10.2 or later Here's a simplified example of what I'm trying to do: ...
2
votes
1answer
58 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 ...
3
votes
2answers
106 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
1answer
353 views

Jumps in NDSolve results

I need to compute using NDSolve routine, some function $F(x)$, having two possible values $F_1(x)$ and $F_2(x)$ depending on whether the argument exceeds some ...
0
votes
0answers
49 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: ...
1
vote
1answer
191 views

Manipulating local or external variable within NDSolve

I am wanting to save and use the value of a variable within NDSolve[] but without that variable being part of the equation itself. Code below (ODE for the Leaky ...
0
votes
1answer
158 views

How to make the plot smooth

There are some stranges point which cause the figure isn't smooth. I think that the reason is the method of numericial integration. Here is my code, it's pleasure that one can revise the drawbacks in ...
7
votes
1answer
278 views

NMinimize with NIntegrate (crash in symbolic evaluation, memory leak)

This is a "common" problem from what I've seen, but with a different spin. I have a function I use often that finds a fit of an expression to another expression with some free parameters (e.g. for ...
0
votes
1answer
82 views

Integrate works but NIntegrate doesn't

I have a complicated integral function that I'm trying to evaluate, which will have to be done numerically. I wanted to try a simpler one first, one that has an analytic form, because I could check ...
2
votes
2answers
94 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 ...
1
vote
0answers
59 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. ...
3
votes
0answers
127 views

Nested NIntegrate of vector function

I am trying to perform a nested integration where the upper limit of the inner integral depends on the value of the outer integral, like in this question: Nested NIntegrate. Just like the linked ...
3
votes
1answer
203 views

Backward in time numerical integration with fixed time step

Consider simple use of NDSolve[] function used to solve an ODE backward in time ...
1
vote
1answer
55 views

NIntegrate option for FourierSeries

I would like to use FourierSeries but it is very slow. My guess is that it is because it uses symbolic integration: ...