Runge: Ueber die numerische Auflösung von Differentialgleichungen

What changed

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.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. 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.

Contributors

• Carl Runge · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Springer DOI record for Runge numerical ODE paper
• Crossref record for Runge numerical ODE paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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