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Wikipedia presents a timeline of important developments in Numerical Methods for ODEs, namely:

1768 - Leonhard Euler publishes his method.
1824 - Augustin Louis Cauchy proves convergence of the Euler method. In this proof, Cauchy uses the implicit Euler method.
1855 - First mention of the multistep methods of John Couch Adams in a letter written by F. Bashforth.
1895 - Carl Runge publishes the first Runge–Kutta method.
1905 - Martin Kutta describes the popular fourth-order Runge–Kutta method.
1910 - Lewis Fry Richardson announces his extrapolation method, Richardson extrapolation.
1952 - Charles F. Curtiss and Joseph Oakland Hirschfelder coin the term stiff equations.

but with no links for the original works.

The question is: are there references with a timeline like this with links pointing to the original works?

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    $\begingroup$ The second "External Link" on the wikipedia page refers to a 1996 thesis by Dominique Tournes and links to reunion.iufm.fr/dep/mathematiques/calculsavant/Equipe/… where the PDFs are available. You will likely find all the references to the original works there along with discussion (though perhaps in French). Just googling "history of numerical methods" brought up this remarkable (though admittedly not what your question is looking for) oral history project of SIAM history.siam.org . $\endgroup$
    – j.c.
    Commented Sep 27, 2012 at 16:58
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    $\begingroup$ Dahlquist's dissertation should be mentioned. $\endgroup$
    – timur
    Commented Sep 27, 2012 at 17:09

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Here are the sources:

Leonhard Euler: Institutiones calculi integralis (1768)

Augustin Louis Cauchy: Cours d'Analyse: Equations différentielles ordinaires et aux dérivées partielles (1824)

The Adams-Bashforth multistep-method as well as the Adams–Moulton methods are described here

Carl Runge: Über die numerische Auflösung von Differentialgleichungen, Math. Ann. 46 (1895) 167-178

W. Kutta: Beitrag zur näherungsweisen Integration totaler Differentialgleichungen, Z. Math. Phys. 46 (1901) 435-453. (Remark: The name is Martin Wilhelm Kutta, the correct year is 1901.)

Lewis Fry Richardson: The approximate arithmetical solution by finite differences of physical problems involving differential equations,with an application to the stresses in a masonry dam Phil. Trans. R. Soc. London Ser. A 210 (1910) 307–57

Of interest in this connection is also E.J. Nyström: Über die numerische Integration von Differentialgleichungen, Acta Soc. Sci. Fennicae 50, 13 (1925) 55

Charles F. Curtiss and Joseph Oakland Hirschfelder: Integration of stiff equations, Proc Natl Acad Sci U S A, 38,3 (1952) 235–243

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