Questions on the use of numerical functions NIntegrate and NDSolve.

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2
votes
1answer
532 views

(NDSolve) Non-linear 2nd order ODE, regular singular point (looking for good methods for this problem)

I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ $$\frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda ...
2
votes
2answers
235 views

Plot result of non analytical-integral

I have the following function: h = 1; c = 1; k = 1; B2 = (2*h*c^2)/(x^5 (Exp[(h*c)/(x*k*T)] - 1)); (someone can see that this integral is the Planck function). ...
2
votes
0answers
2k views

NDSolve: methods and step size choosing

I am looking into the documentation of NDSolve[]; more precisely how this function chooses the StepSize and how it chooses which ...
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
1answer
105 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. ...
1
vote
1answer
279 views

Slow evaluation of NIntegrate when used as a pure function

I asked a perhaps related question here. Here is my code in below. The goal is that to define a function which must be integrated numerically. The function itself first is calculated over different ...
0
votes
1answer
135 views

More issues Integrate, NIntegrate, FindRoot

I'm trying to solve a system of 3 non-linear equations using FindRoot and Integrate. If I start FindRoot[] close to the right answer, it works well but returns a bunch of error messages first. ...
-3
votes
1answer
153 views

Integration with mathematica? [closed]

I am very new to Mathematica. I am trying to evaluate ∫ (1+lnx)Sqrt(1+(xlnx)^2) using Mathematica. I know a substitution must be done so I have set ...
20
votes
4answers
2k views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
14
votes
1answer
600 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
14
votes
1answer
302 views

Inconsistent behavior of WhenEvent[ ]

Consider the following simple example: ...
3
votes
2answers
930 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
13
votes
3answers
1k views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
5
votes
1answer
365 views

NDSolve and WhenEvent Causing Excess Work

When I use the following system model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5} with the ...
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: ...
8
votes
1answer
446 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
5
votes
2answers
160 views

How to speed up Integration of interpolation function?

I have a list of data, and I interpolate it to a function. Then I need to do an integration with the interpolating function. But I found that the speed is unacceptably slow. My data is here (a little ...
4
votes
1answer
1k views

Monitoring the Evaluation of NDSolve: time to finish estimation

My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
8
votes
1answer
268 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
7
votes
2answers
261 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: ...
7
votes
2answers
1k views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
5
votes
2answers
154 views

Example of Integrate applying a numerical evaluation N

Here is a minimal example: Integrate[(a[1] + x)^2, {x, 1., 2.}] 2.33333 + 3. a[1.] + 1. a[1.]^2 The problem is that ...
5
votes
5answers
1k views

NIntegrate::slwcon Problem

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate[] needs a lot of time to calculate this. Is there any way to ...
5
votes
2answers
879 views

Animating the Lorenz Equations

I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck. The equations are: ...
5
votes
1answer
1k views

Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?

I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs: ...
4
votes
2answers
570 views

BC for transport equation using NDSolve

First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
4
votes
1answer
655 views

Multiple simultaneous events in EventLocator method for NDSolve

I'm using NDSolve to integrate a system of ODEs, and EventLocator to stop the integration when it leaves a certain region in phase space. This works perfectly as it should. However, I've also added ...
2
votes
3answers
169 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 ...
1
vote
1answer
299 views

Locating Periodic Orbits

Here is the code for the numerical integration of an orbit. First the module for the definition of the equations of motion. ...
1
vote
1answer
1k views

NIntegrate & non-numerical values

I am wondering why I am receiving the message "The integrand ... has evaluated to non-numerical values for all sampling points in the region ..." for a particular calculation I am running. How can I ...
16
votes
1answer
3k views

Parallelizing Numerical Integration in Mathematica

I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
12
votes
1answer
428 views

Boosting the performance of expensive NIntegrate by feeding in a cheap approximation of the integrand

I need to integrate an expensive likelihood L[x] over its n-dimensional domain. I know that L[x] is decently approximated by a ...
10
votes
2answers
296 views

How to use NDSolve with discontinuities at internal boundaries?

I don’t know how to impose discontinuous internal boundary conditions (BCs) in NDSolve, so I’ve set up an example problem to illustrate my issue. Consider the simple first-order ODE for $f(z)$ on the ...
10
votes
1answer
244 views

Is this a bug in NIntegrate?

Fixed in 10.1 Bug is present as of version 10.0.2 checked on windows 7, 64 bit Is this a bug or I missed something? NIntegrate seems to give a different ...
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 ...
9
votes
2answers
550 views

Why do I get a different value when I change the order of integration?

I think the following two-dimensional integrals should be equal, since they both integrate the function over the half plane defined by $t>\tau$. $$\int_{-\infty}^\infty \mathrm{d}t ...
9
votes
1answer
341 views

The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
8
votes
2answers
343 views

What's wrong with NIntegrate with “MonteCarlo” Method?

Bug fixed in version 10.2.0 My code is: ...
8
votes
2answers
537 views

Monte Carlo integration with random numbers generated from a Gaussian distribution

I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know. How can I change ...
8
votes
1answer
1k views

Efficient evaluation of functions defined by NIntegrate

I have a complicated function $f$ and I want to plot the function $F(x)$ defined by the definite integral of $f$ from $0$ to $x$: $$ F(x) = \int_0^x f(y)\mathrm dy. $$ Apparently $f$ cannot be ...
7
votes
2answers
171 views

Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
7
votes
1answer
124 views

Unify the sampling of NIntegrate[ {f, g, h} w ]

I'm trying to numerically integrate a function which has a vector-valued slow part and a much faster component which is shared by all the components, i.e. an integral of the form $$ ...
6
votes
2answers
563 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a piecewise function. If we define the ODE system ...
6
votes
1answer
911 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
6
votes
2answers
5k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
5
votes
4answers
247 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: ...
5
votes
1answer
93 views

In a PDE solution let us integrate out one of two coordinates

Here is a trapezoid within which I am solving a simple Laplace equation with the Dirichlet boundary conditions set at its top and bottom: ...
5
votes
1answer
406 views

Numerical solution of IVP for linear ODE with variable coefficient runs wild soon

Cross posted in scicomp.SE. A friend of mine showed me this initial value problem (IVP) for a linear ordinary differential equation (ODE) with variable coefficient: $$y''(x)=\left(x^2-1\right) ...
5
votes
1answer
375 views

Obtaining an NIntegrate error estimate

Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate? Internally Mathematica must keep track of ...
5
votes
1answer
251 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; ...