Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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0answers
199 views

How can one use differential boundary conditions with helmholzSolve?

I can not get the helmholzSolve function provided by Mark McClure and user21 to work for a case that I want to constrain the spacial derivative of a boundary. In ...
1
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1answer
117 views

Speeding up Integrate and the numerical solution

I want to compute the drag of a plate Below is the code I am using to integrate the function ...
1
vote
1answer
71 views

How can I combine NIntegrate with NDSolve?

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
1
vote
0answers
92 views

Problem setting boundary conditions with NDSolve [closed]

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu ...
3
votes
1answer
870 views

Singular integral: NIntegrate fails to converge

I need to calculate the following singular integral: NIntegrate[Log[1 + y^2]/Cos[Pi y], {y, 0, 1}] However, it is failing to converge. I have tried to specify ...
0
votes
2answers
69 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: ...
7
votes
2answers
374 views

How much time should one give Mathematica for an integral evaluation?

Sometimes when I do integrals in Mathematica (M), it keeps thinking and thinking and I have no idea what is going on inside M. For how long should one wait or how does one know whether M has not got ...
4
votes
2answers
93 views

How should I evaluate the numerical integral of a function with divergent part substracted?

I want to evaluate the following integral numerically in Mathematica, $$\int_0^{\infty}(\frac{1}{(1 - e^t)^{10}} - (\frac{1}{t^{10}} - \frac{5}{t^9} + \frac{145}{12 t^8} - \frac{75}{ 4 t^7} + ...
16
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 ...
0
votes
0answers
53 views

NIntegrate some kind of highly oscillatory function

I have an analytical expression (exp) like this, See here. It is a kind of highly oscillatory function for (x1,x2,x3,x4). So,how to get the integral result by ...
0
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0answers
43 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 ...
5
votes
2answers
155 views

Why am I getting different answers for an integral depending on method?

I'm trying to carry out an integral and I'm finding different answers depending on which method I choose to integrate with. I assume this has something to do with divergent pieces but I don't ...
0
votes
0answers
49 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 ...
7
votes
2answers
241 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: ...
1
vote
1answer
169 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 ...
2
votes
2answers
107 views
9
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1answer
1k views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
4
votes
0answers
64 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 ...
1
vote
1answer
56 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 ...
5
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1answer
70 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 ...
11
votes
1answer
260 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 - ...
2
votes
0answers
57 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
85 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
195 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
162 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 ...
0
votes
1answer
134 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
581 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
58 views
3
votes
2answers
192 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
52 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
97 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
108 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
382 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
255 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
76 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
252 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
269 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. ...
-1
votes
1answer
268 views
2
votes
0answers
129 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
78 views

Convergence in NIntegrate

I wish to understand how to cope with the following error messages: ...
2
votes
2answers
222 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
73 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
683 views
7
votes
1answer
871 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 ...