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

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8

Finite difference schemes

8.1  Finite differences

The opening line of Anna Karenina, ‘All happy families resemble one another, but each unhappy family is unhappy in its own way’,1 is a useful metaphor for the computation of ordinary differential equations (ODEs) as compared with that of partial differential equations (PDEs). Ordinary differential equations are a happy family; perhaps they do not resemble each other but, at the very least, we can write them in a single overarching form y′ = f(t, y) and treat them by a relatively small compendium ...

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