# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### 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 ...
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### NIntegrate vs. summation

I' m interesting in distributions of points on sphere, plane figures etc. Especially for small number of points: 1, 3, 7, ... It seems that good criterion for uniformity of distribution is some ...
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### Integration does not give real value

The code below must be obvious. We are trying to integrate a complicated function from 0 to 1. ...
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### Problem with FindMinimum

I am struggling with a problem on fitting a function to my data using FindMinimum. The problem is related to small angle x-ray scattering and my approach is the following: I define the electron ...
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### Problems using a complicated function within a LogLinearPlot [duplicate]

my problem is that I have a rather large function which I'm trying to plot, which looks something like this: ...
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### How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by <...
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### What boundary is added when NDSolve::bcart pops up?

When insufficient boundary conditions are given to NDSolve for solving PDE, the warning NDSolve::bcart pops up: ...
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### optimization of CountourPlot with NIntegrate

I have to use ContourPlot with a complicated function depending on 2 parametrs (that I cannot report here) that contains numerical integrations. Here is a simple ...
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### Inefficient NIntegrate and Which

In version 10 a simple numerical integraton of piecewise function is highly inefficient: ...
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### Precision of NIntegrate

At the moment I am considering a "difficult", highly-oscillatory integral in Mathematica. It calculates the integral without any complaints. However, I am also trying out a numerical method with which ...
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### NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
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### Implicit region misses subset?

Context I am interested in integrating a 2D function over lines defined implicitely Attempt Let me just start by integrating the identify on such sets of lines which a defined using ...
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### Integrate over implicit 1D region: works for algebraic but not transcendental equation?

QUESTION How come this works: NIntegrate[1, {x, y} ∈ ImplicitRegion[{x == y^3, x <= 1, x >= 0}, {x, y}]] But this fails: ...
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### Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
282 views

### Solving a nasty partial differential equation

I have a differential equation that I would like to solve numerically in the region $z \in [0,L]$ and $t \in [0,t_{max}]$: $$\partial_t S(z,t) = f(z)S(z,t) + \int_0^L \text{d} z'g(z,z') S(z',t),$$ ...
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### What method does NIntegrate use by default?

There is a variety of algorithms for performing numerical integration (See wiki). What method does NIntegrate use by default? I looked at the documentation page ...
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### NIntegrate and Integrate of a Spherical Bessel function

I am trying to integrate a spherical Bessel function. I have used both the Integrate and NIntegrate functions in Mathematica but ...
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### How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
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### How to obtain numerical answer for equation containing integration

Could some one tell me how to obtain numerical value of $a$ and $b$ from equations below: $$\frac{1+exp(b)}{1+exp(0.9a+b)}=0.95$$ $$\int_{0}^{\infty} \frac{1+exp(b)}{1+exp(a x+b)}=1$$
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### Finding the true expectation

I have the density function and I want to determine its expected value ...
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### Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
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### Numerical Integration/Function

I have a problem with a function defined numerically through an integral of the form: ...
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### What means the definition F[t_?NumericQ] :=…? [duplicate]

I've come along a function defined in this way: F[t_?NumericQ] := NDSolve[{-u''[x] - u[x]/x == -t^2 u[x], u[x0] == x0, u'[x0] == 1}, u, {x, x0, x1}] What does ...
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### Runge-Kutta Butcher tables

I like to have the Butcher's table for Explicit (or implicit as well) Runge-Kutta method of a fixed order. I do not understand reading http://blog.wolframalpha.com/2013/09/10/numerical-methods-runge-...
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### NDSolve not able to solve a system of differential equations

Here are some basic equations ...
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### NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
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### Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
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### Integral for piecewise function inconsistent with the usual way

I have the following piecewise function: ...
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### WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
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### Double application of NIntegrate produces unexpected error messages [duplicate]

In the course of trying to answer 69601, I encountered unexpected error messages. In highly simplified form, NIntegrate[NIntegrate[z y, {y, 0, 10}], {z, 0, 10}] ...
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### Two dimensional high oscillated numerical integral

I have some problem with two dimensional integral. I want to calculate such integral. ...
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### Complex Integration

There are some sequential functions: ...
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### How to ensure efficient order of operations for rules, slots, substitutions?

I need to calculate several functionals Q[[t]] of a pdf f[x]. ...
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### Incomplete Integration in Area

Area[2 Sqrt[(1 - p^2)^2 - r^2], {p, 0, 1}, {r, 0, 1 - p^2}] is able to perform only the integral over r, leaving the integral ...
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### NIntegrate with units: unable to determine the units of quanitites that appear in the input

I want to integrate Planck's law of radiation in a certain wavelength intervall with units. I define some constants: ...
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### Summand is not numerical at some point

I am trying to do some numerical integration with the following codes: ...
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### How to use slots and patterns to reduce repetitive calculation?

This is kind of complicated... How can we make MMa calculate values of a function before doing multiple pattern or slot substitutions? Answers to similar questions didn't cover the case where the ...
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### Numerical integration with symbolic coefficients

Thanks to Michael and its reply here I managed to deal with some of the more complicated integrals. But still there are some even more complicated ones. Let give a specific example. ...