Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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0answers
75 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
872 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
119 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
312 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
200 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
74 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
180 views

Solving non-linear differential equation

For my research project I need to solve the following integral ...
1
vote
2answers
121 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
845 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
120 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
235 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
57 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
350 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
187 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
272 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
93 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
58 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
122 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
189 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
52 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: ...
4
votes
2answers
193 views

How to speed up a high dimensional numerical integration of Gaussian-form integrand [duplicate]

My integral has the following form: $$\int \sin(\theta) d\theta d\phi\left| \int d^3p_1 d^3p_2d^3p_3 \frac{f(p,\theta,\phi)}{g(p,\theta,\phi)}e^{-\frac{1}{2}(p^\mathrm{T} .A.p)}\right |^2,$$ where ...
2
votes
1answer
148 views

NDSolve with different function lengths over time

I'm working on a cops & robbers game, and there is one single event that is very very important, the event of catching someone. I'm trying to do when any robber is catched, delete it from the ...
2
votes
1answer
1k views

NDSolve two PDE plus one ODE, together

I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
1
vote
2answers
138 views

How to determine the parameter in a differential equation with some fixed solution

Assuming that I have a ODE system with undetermined parameter $$x''(t) == y(t) x(t)$$ $$y'(t) == 2 - a x(t)$$ and I have some fixed solution condition $$x(0)=0$$ $$x(10)=8$$ $$y(10)=3.5$$ Is there ...
1
vote
2answers
168 views

How do I exclude regions from numeric integration on Mathematica?

The part of the equation that is giving me trouble is below: f[t_,v_]:= Exp[-(1/Log[1-t/v]^2)]*(v-t) I need to integrate this function over the ranges .1 ...
7
votes
2answers
225 views

How to do multi-dimensional principal value integration?

The toy model is: $$\int_{-2}^{2}\int_{-2}^{2}\frac{1}{1-(x^2+y^2)}\, dx\, dy$$ The integrand have opposite sign across the circle $x^2+y^2=1$, so one would expect that the integral has meaning only ...
3
votes
0answers
122 views

NSolve doesn't work on an equation containing a numerical integral and constraints

I'm having trouble getting Mathematica to solve equations numerically. I know that its important to specify the type of variables for pattern testing (see e.g. here) but this doesn't seem to work. ...
3
votes
2answers
154 views

Maximizing a function defined using NIntegrate [duplicate]

I have two functions fn[x,y,z] which is in integral form and I have another function gn[x,y] which is also in integral form ...
3
votes
2answers
707 views

Unexpected result of summation

I wrote a small module that gives me an incorrect output-set. It should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
10
votes
1answer
94 views

How to speed up the evaluation of a function with a large LeafCount but many repeated sub-functions for use in NIntegrate

General Context Apparently, the memory leak in NIntegrate is unavoidable pre-MMA-10.2. I have some (two-dimensional) numerical integration to do on a complicated ...
1
vote
2answers
141 views

Numerical integration of modified bessel function

I need to compute the following integral: NIntegrate[ BesselI[-nu, k x]/x ,{x, r1, r}] in which nu=-(2m-1)/2 and I have to ...
2
votes
1answer
93 views

Three Dimensional Plot of Numerical Integral with Delta Function

I want to plot the definite integral of the following function ...
1
vote
0answers
61 views

Plotting roots for a singular numerically-only integrable equation [closed]

In my problem I need to plot roots with respect to a parameter. But the condition for root is det(Function)=0. This function cannot be solved symbolically. So I need to put in a parameter value and ...
2
votes
3answers
168 views

slwcon and eincr in integrating multivariate Gaussian random variables

Why is the following integration involving multivariate Gaussian distribution so slow and generating an error? Is there a better integration strategy? All that I'm doing is considering ...
2
votes
0answers
96 views

Nasty integral advice

I have a pretty ferocious integral to solve, and since it doesn't seem I'll be able to do much analytically, I've taken to Mathematica to get some information. Mainly, I want to see if there are any ...
4
votes
2answers
254 views

Postprocessing of CFD results in Mathematica

I was trying to perform computational fluid dynamics (CFD) post-processing in Mathematica after solving primitive variables from Navier-Stokes equation, mainly $(u,v)$, $(Px,Py)$. Since I am not an ...
0
votes
1answer
89 views

NIntegrate and memory use [duplicate]

I wonder why NIntegrate uses memory. I have a long integral computation repeated thousands times. The memory use then goes up and speed goes down. I think I spot a ...