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

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7

Nonlinear algebraic systems

7.1  Functional iteration

From the point of view of a numerical mathematician, which we adopted in Chapters 15, the solution of ordinary differential equations is all about analysis – i.e. convergence, order, stability and an endless progression of theorems and proofs. The outlook of Chapter 6 parallels that of a software engineer, being concerned with the correct assembly of computational components and with choosing the step sequence dynamically. Computers, however, are engaged neither in analysis nor in algorithm ...

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