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The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable
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Orientador(es)
Resumo(s)
Let (®, ¯) ½ R denote the maximal interval of existence of
solution for the initial-value problem
½ dx
dt = f(t, x), f : E ! Rm,E is an open subset of Rm+1
x(t0) = x0, with (t0, x0) 2 E.
We show that (®, ¯) is r.e. (recursively enumerable) open and the solution
x(t) defined on (®, ¯) is computable, provided that (a) f is computable
and effectively locally Lipschitz, and (b) (t0, x0) is a computable point.
We also prove that this result is the best in the sense that, for some
initial-value problems satisfying (a) and (b), their maximal intervals of
existence are non-recursive.