Computability on reals, infinite limits and differential equations

DOI10.1016/j.amc.2007.02.146zbMath1193.03083OpenAlexW2153355623MaRDI QIDQ990444

Jerzy Mycka, Bruno Loff, Costa, José Félix

Publication date: 1 September 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2007.02.146

zbMATH Keywords

differential equationscomputability on realsreal recursive functionsinfinite limits

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Numerical methods for ordinary differential equations (65L99)

Related Items (3)

A survey of recursive analysis and Moore's notion of real computation ⋮ A foundation for real recursive function theory ⋮ A Survey on Analog Models of Computation

Cites Work

• Real recursive functions and their hierarchy
• A new conceptual framework for analog computation
• The existence of noncollision singularities in Newtonian systems
• Classical recursion theory. Vol. II
• Recursion theory on the reals and continuous-time computation
• \(\mu\)-recursion and infinite limits.
• Analog computers and recursive functions over the reals.
• The differential analyzer. A new machine for solving differential equations
• An analog characterization of the Grzegorczyk hierarchy
• The P\(\neq\) NP conjecture in the context of real and complex analysis
• The many forms of hypercomputation
• Church's thesis meets the \(N\)-body problem
• Elementarily computable functions over the real numbers and \(\mathbb R\)-sub-recursive functions
• Undecidability over Continuous Time
• Extremal solutions of a discontinuous scalar differential equation
• Hilbert's Tenth Problem is Unsolvable
• Infinite time Turing machines
• On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines
• Simplifications of the recursion scheme
• Machines, Computations, and Universality
• Mathematical Theory of the Differential Analyzer
• Iteration, inequalities, and differentiability in analog computers
• On the Cauchy problem for first order discontinuous ordinary differential equations
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