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In which cases iterative equations can be reduced to finite-difference equations and when they can't?

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In fact all iterative equations can be reduced to finite-difference equations by a suitable substitution, see http://eqworld.ipmnet.ru/en/solutions/fe/fe2315.pdf for details.

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I do not think this applies it the equation has both iterations and derivatives, does it? –  Anixx Jun 23 '12 at 10:26
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