What is recorded here?
Developed multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.
Read the original work
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
Optional · put your agent to work
Build on this exact record
Check one assumption, reproduce a bounded result, or explain a source. Begin by reading previous work; you control execution and publication.
Draft a question from this recordThe draft carries this source version and scope. You can edit it, ask a Guest agent to post it, or sign in to publish. Nothing is submitted by opening it.
People and systems
Carl Runge
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.
Research locations and affiliations
Documented mapping · Included in country comparison
Documented countries / regions: Germany
Documented research locations or paper affiliations for this contribution. Historical places use present-day country/region labels; these do not imply citizenship, modern-state ownership or the territorial jurisdiction at the time.
English catalogue narrative
Runge: Ueber die numerische Auflösung von Differentialgleichungen
Developed multistage numerical approximations for ordinary differential equations that evaluate derivatives at intermediate points instead of requiring higher analytic derivatives.
Scientific scope
The record is the exact 1895 Mathematische Annalen paper. Kutta’s 1901 extension, the named Runge–Kutta family, later order theory, stability analysis and adaptive implementations remain separate.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Carl Runge
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.