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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles

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6.1  Numerical software vs. numerical mathematics

There comes a point in every exposition of numerical analysis when the theme shifts from the familiar mathematical progression of definitions, theorems and proofs to the actual ways and means whereby computational algorithms are implemented. This point is sometimes accompanied by an air of anguish and perhaps disdain: we abandon the palace of the Queen of Sciences for the lowly shop floor of a software engineer. Nothing could be further from the truth! Devising an algorithm that ...

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