Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-kfj7r Total loading time: 0.349 Render date: 2022-12-03T09:14:27.525Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

On Runge-Kutta processes of high order

Published online by Cambridge University Press:  09 April 2009

J. C. Butcher
Affiliation:
University of Canterbury, New Zealand.
Rights & Permissions[Opens in a new window]

Extract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An (explicit) Runge-Kutta process is a means of numerically solving the differential equation , at the point x = x0+h, where y, f may be vectors.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Butcher, J. C., Coefficients for the study of Runge-Kutta integration processes, This Journal 3 (1963), 185201.Google Scholar
[2]Kutta, W., Beitrag zur näherungsweisen Integration totaler Differentialgleichungen, Zeit. Math. Physik 46 (1901), 435452Google Scholar
[3]Nyström, E. J., Über die numerische Integration von Differentialgleichungen, Acta Soc. Sci. Fennicae 50, No. 13 (1925).Google Scholar
[4]Huta, A., Une amélioration de la méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premier ordre, Acta Fac. Nat. Univ. Commenian. Math. 1 (1956) 201224.Google Scholar
[5]Huta, A., Contribution à la formule de sixième ordre dans la méthode de Runge-Kutta-Nyström, Acta Fac. Nat. Univ. Comenian. Math. 2 (1957), 2124.Google Scholar
[6]Butcher, J. C., On the integration processes of A. Huta, This Journal 3 (1963), 202206.Google Scholar
[7]Butcher, J. C., Integration processes based on Radau quadrature formulas, Math. Comp., 18 (04, 1964).CrossRefGoogle Scholar
[8]Butcher, J. C., Implicit Runge-Kutta processes, Math. Comp., 18 (1964), 5064.CrossRefGoogle Scholar
You have Access
218
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

On Runge-Kutta processes of high order
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

On Runge-Kutta processes of high order
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

On Runge-Kutta processes of high order
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *