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3 Answers

This (site about numerical methods for differential equations) seems to be a good resource.

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A bit late, but... learning the state-of-the-art would warrant reading the two volumes of Solving Ordinary Differential Equations by Hairer, Wanner (and Nørsett); one for nonstiff problems, and one for stiff problems. The bibliography should be able to point you to the other useful books, including Bill Gear's classic.

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I am not sure what you mean by system of differential equations. I would recommend this book. It covers a good amount of numerical analysis for ODE's and PDE's. It has a good amount of problems and illustrations and is fairly rigorous.

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