# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### nintegrate: greater accuracy possible

I've got the following piece of code: ...
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### Understanding difference between NIntegrate result and home-cooked Simpson's rule

In this question I am asking about the different results I get between NIntegrate-ing a function of two variables vs. "doing it myself" with my own implementation ...
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### Numerical integration of some oscillatory function [closed]

I solved numerically an equation in the complex plane. I have the numerical solution, and I want to take its integral on the real axis. For instance, the real part of the solution looks like this: ...
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### Difference between using NIntegrate and Integrate inside NDSolve?

The differential equation I am considering depends on an integral, which I would like to solve with NIntegrate (since it will gets more complicated and thus I have to use NIntegrate later). My code ...
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### How to speed up the plot of NIntegrate?

Here is a toy example: f[t_] := NIntegrate[Sin[x], {x, 0, t}]; Plot[f[t], {t, 0, 10}] // Timing Even such a simple example will take 2.8 seconds on my computer. ...
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### Mathematica will not run Arnoldi method while using NIntegrate

This is simplified version of my real code: ...
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### Numerical integral of finite valued function over finite integral fails with NIntegrate::inumri

I have the following (simplified) integral: ...
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### Double Integral with NDSolve!

I have fivefold multiple integral and I wanted a speed calculations.I came across on this Question and had already begun the problems. Here is a toy example with simple double integral: ...
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### Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
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### In NDSolve, how to involve in the odes a integration function that depends on ode functions and can't be analytically integrated?

I think it would be better to use this simple code to explain my questions: ...
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### NIntegrate evaluates its 1st argument while it has the attribute HoldAll?

NIntegrate owns the attribute HoldAll: Attributes@NIntegrate (* {HoldAll, Protected} *) ...
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### Launching specific remote kernels in parallel

For some reason I found that my numerical integration runs much faster on Mathematica 9 than on Mathematica 10. Since I sent my calculation to a cluster with 24 cores with the following command <...
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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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### Why NIntegrate is badly-behaved on $J_{\frac{9}{2}}(x)$ by default?

A friend of mine showed me this example: Plot[BesselJ[9/2, x], {x, 0, 1}, PlotLabel -> Style["The integrand seems to be simple", 14]] ...
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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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### Integrate on a contour in the complex plane

I want to integrate the function f[z]= z + Conjugate[z] over a circle of radius 2 centered at the origin. For the sake of stating something that I have tried: <...
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### Definite and indefinite integral give different results

I'm trying to find an expression that, given $x$, $y$, and $R$, gives the indefinite 2D integral of a function at the circle centered on $(x_0, y_0)$ with radius $R$. With $g$ as defined below, I'd ...
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### NIntegrate fails in a very strange way

I found a strange behavior in Mathematica when trying to evaluate the integral $$f(n) = \int_{1}^2 \frac{\Gamma(n)\Gamma(x)}{\Gamma(x+n)}{\rm d}x$$ I evaluate this using ...
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### Negative numerical result when integrating a strictly non-negative integrand

Although there are similar posts here Negative integral of a positive function , Positive integrand giving negative answer , my case is even more surprising. I have a very simple function ...
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### Definite Integral. Perfomance problem

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral. In Mathematica 4 the result of the following code ...
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### NIntegrate: Random occurance of “Catastrophic loss of precision” error

I have the following integral: ...
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### How to solve an iterative integral equation for a function in Mathematica 8.0?

I would like to solve the following iterative integral equation in order to find the functional form of $P_{0}(k)$ numerically and then use it subsequently for the rest of my code: ...