https://github.com/abarbour/kelvin
Solutions to the the Kelvin differential equation in R:
Science Score: 10.0%
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Repository
Solutions to the the Kelvin differential equation in R:
Basic Info
- Host: GitHub
- Owner: abarbour
- Language: HTML
- Default Branch: master
- Homepage: https://cran.r-project.org/package=kelvin
- Size: 3.75 MB
Statistics
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
kelvin
Solutions to the the Kelvin differential equation in R
by Andrew J Barbour
<!-- badges: end -->
Calculation of solutions to the Kelvin Differential Equation
using Bessel functions namely
BesselJ and BesselK from the Bessel package.
Background information
The following is taken from Wolfram:
Kelvin defined the Kelvin functions bei and ber according to
ber_v(x) + i*bei_v(x)
= J_v(x*exp(2*pi*i/4))
= exp(v*pi*i)*J_v(x*exp(-pi*i/4))
= exp(v*pi*i/2)*I_v(x*exp(pi*i/4))
= exp(3*v*pi*i/2)*I_v(x*exp(-3*pi*i/4))
where J_v(x) is a Bessel function of the first kind and I_v(x)
is a modified Bessel function of the first kind. These functions satisfy the
Kelvin differential equation.
Similarly, the functions kei and ker by
ker_v(x) + i*kei_v(x) = exp(-v*pi*i/2)*K_v(x*exp(pi*i/4))
where K_v(x) is a modified Bessel function of the second kind.
For the special case v=0,
J_0(i*sqrt(i)*x)
= J_0(sqrt(2)*(i-1)*x/2)
= ber(x) + i*bei(x)
Owner
- Name: Andy Barbour
- Login: abarbour
- Kind: user
- Location: Menlo Park, CA
- Company: @usgs
- Website: http://www.andybarbour.com
- Repositories: 11
- Profile: https://github.com/abarbour
GitHub Events
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- Push event: 9
- Create event: 1
Last Year
- Push event: 9
- Create event: 1
Committers
Last synced: 8 months ago
Top Committers
| Name | Commits | |
|---|---|---|
| Andy Barbour | a****r@g****m | 65 |
| Andy Barbour | a****r@u****u | 10 |
Committer Domains (Top 20 + Academic)
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Last synced: 7 months ago
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Packages
- Total packages: 1
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Total downloads:
- cran 229 last-month
- Total docker downloads: 42,005
- Total dependent packages: 1
- Total dependent repositories: 2
- Total versions: 6
- Total maintainers: 1
cran.r-project.org: kelvin
Calculate Solutions to the Kelvin Differential Equation using Bessel Functions
- Homepage: https://github.com/abarbour/kelvin
- Documentation: http://cran.r-project.org/web/packages/kelvin/kelvin.pdf
- License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
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Latest release: 2.0-3
published 11 months ago
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Maintainers (1)
Dependencies
- R >= 2.10.1 depends
- Bessel >= 0.5 imports
- knitr * suggests
- rmarkdown * suggests
- testthat * suggests