Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
84 questions from the last 365 days
2
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146
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Numerically integrate an implicit vector vectorizedly
I want to define a function f[x] and then be able to integrate numerically as a vector - not component by component. The following is my failed attempt:
...
- 169
3
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2
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226
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Solving a coupled 2nd order differential equation numerically using NDSolve
I would like to solve the following system of differential equations numerically for two one-dimensional functions $R(x)$ and $\phi(x)$:
\begin{eqnarray}
c_1 \left(R''(x) - (\phi'(x))^2 R(x) \right) - ...
- 93
2
votes
0
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61
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how to improve the predictor corrector schemes including computational cost
I am currently implementing a variable-order fractional predictor–corrector scheme in Mathematica. Since I am still a beginner with Mathematica programming, I encountered several issues during the ...
3
votes
1
answer
183
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Mathematica ODE question
I am trying to solve an iterative matrix ODE of the form $f_k'(x)=T.f_k(x)+B(x)*S.f_{k-1}(x)$, where f is an $n$ dimension column, T and S are $n \times n$ matrices, and $B(x)$ is a function. The ...
- 169
0
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1
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160
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NIntegrate on apparently simple function returning convergence issues
I am looking for a help in numerically integrating this function:
...
- 651
2
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0
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74
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Event is not triggered in NDSolve
I'm solving an ODE system with multiple events and find the discrete variable not updated as expected because one of the events is not triggered. During narrowing down the problem, I find something ...
- 1,277
4
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2
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370
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Fluctuating results with NIntegrate
I've been trying to calculate an integral using NIntegrate as follows.
...
- 43
3
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0
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125
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Efficiently Finding Optimal Configurations of Lofted Solids
A lofted solid is like a solid cylinder with two different end caps.
A natural set of questions given a lofted solid using two shapes would be if we were to be able to rotate an end around the ends ...
- 687
0
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104
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How to integrate this highly singular function?
I have a function $f(z,\bar{z})$ that I would like to eventually integrate over the whole complex plane $\mathbb{C}$ parametrized by $(z,\bar{z})$. The function $f(z,\bar{z})$ has a singularity near $...
- 21
5
votes
2
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314
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NDSolve exceedingly slow
I the following ODE with parameters
\begin{align}
B_e\: \theta''(s)+2(s-1)\cos\theta(s)=S_e\: f\left(\theta(s)\right),
\end{align}
with $0\leq s\leq 1$ and
\begin{align}
\theta(0)=0\:\:\:\text{and}\:\:...
- 806
7
votes
2
answers
405
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Strange issue with numerical integration
I have mathematica 14.3.
I have encountered a weird issue when numerically integrating this complicated function
...
- 259
3
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1
answer
197
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circumventing apparent errors in Integrate and NIntegrate
I have been working on a wiki page about asymptotic Laurent series for derangements, and recently learned that the converse of Watson's lemma often holds, allowing one to represent such series as ...
- 151
1
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1
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160
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How should I deal with some unexpected values in numerical integration?
I computed the following numerical integration, which contains some unexpected points. How to revisit it?
...
- 111
1
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2
answers
177
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Numerical integration with Singularity
I have an integral that I want to integrate over the whole $\mathbb{C}$ plane, say parametrized by $(z,\bar{z})$. The integrand is of the following form
$$ \frac{f(z,\bar{z})}{|1-z|^2} - \frac{C}{|1-z|...
- 21
0
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1
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179
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Equivalent integrals, different answers
Below are two equivalent definite integrals.
$$\begin{align*}S&=2\pi\int_0^\pi b\sin t\sqrt{a^2\sin^2t+b^2\cos^2t}\text dt\\
&=4\pi b\int_0^\frac{\pi}{2}\sin t\sqrt{a^2-(a^2-b^2)\cos^2t}\text ...
- 101