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Book on numerical solution of PDEs
Michael Zingale has written a rather extensive open-source textbook on numerically solving PDEs, albeit with an astrophysical context (which shouldn't really matter, the methods are largely the same), ...
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Book on numerical solution of PDEs
If you just want to get hands-on and actually solve problems, then try this book freely available online.
Finite Difference Computing with Partial Differential Equations
Hans Petter Langtangen
There ...
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