Computable analysis: an introduction
Computable analysis: an introduction
A Simple and Powerful Approach for Studying Constructivity, Computability, and Complexity
Constructivity in Computer Science, Summer Symposium
Computability theory of generalized functions
Journal of the ACM (JACM)
Computing Schrödinger propagators on Type-2 Turing machines
Journal of Complexity
Computable Analysis of the Abstract Cauchy Problem in a Banach Space and Its Applications (I)
Electronic Notes in Theoretical Computer Science (ENTCS)
Computing the Solution of the m-Korteweg-de Vries Equation on Turing Machines
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Computing Solutions of Symmetric Hyperbolic Systems of PDE's
Electronic Notes in Theoretical Computer Science (ENTCS)
Beyond the first main theorem – when is the solution of a linear cauchy problem computable?
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Computable analysis of a non-homogeneous boundary-value problem for the korteweg-de vries equation
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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In this paper we answer an open question raised by Pour-El and Richards: Is the solution operator of the Korteweg-de Vries (KdV) equation computable? The initial value problem of the KdV equation posed on the real line R: ut + uux + uxxx = O, t, x ∈ R, u(x, 0) = ϕ(x) defines a nonlinear map KR from the space Hs (R) to the space C(R; Hs(R)) for real numbers s≥ 0. We prove that for any integer s ≥ 3, the map KR : Hs (R) → C(R; Hs (R)) is Turing computable.