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I am searching for a reference book that details numerical methods for solving differential equations, their rate (order) of convergence, their cost, and if possible some applications.

Any suggestion is appreciated.

Thank you in advance.

Edit: solving partial differential equations.

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marked as duplicate by Jack D'Aurizio Mar 13 '18 at 16:10

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    $\begingroup$ Ordinary differential equations? Partial differential equations? $\endgroup$ – Michael Lee Mar 13 '18 at 15:26
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    $\begingroup$ Although your question is not specific on ODEs vs. PDEs, look into 1. Numerical Methods for Ordinary Differential Equations 3rd Edition by J. C. Butcher, 2. Solving Ordinary Differential Equations I: Nonstiff Problems by Ernst Hairer,‎ Syvert P. Nørsett,‎ Gerhard Wanner, 3. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. There are many others, but those are worth a look. $\endgroup$ – Moo Mar 13 '18 at 15:43
  • $\begingroup$ You should have been explicit upfront. Solving ODEs and PDEs are completely different matters. $\endgroup$ – Yves Daoust Mar 13 '18 at 15:52
  • $\begingroup$ @Nizar: I am not as familiar with PDEs, but you might want to peruse the books given Google $\endgroup$ – Moo Mar 13 '18 at 15:55