A computable ordinary differential equation which possesses no computable solution
نویسندگان
چکیده
منابع مشابه
An ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable
Let (α, β) ⊂ R denote the maximal interval of existence of solution for the initial-value problem
متن کاملComputable Analysis of the Solution of the Nonlinear Kawahara Equation
In this paper, we study the computability of the solution operator of the initial problem for the nonlinear Kawahara equation, which is based on the Type-2 Turing machines. We will prove that in Sobolev space 2 ( ) s H R , for 0 s ≥ , the solution operator: 2 : ( ) s R K H R → ( ; C R 2 ( )) s H R is ( ,[ s H δ ρ → ]) s H δ -computable. The conclusion enriches the theory of computability. Key w...
متن کاملCharacterizing Computable Analysis with Differential Equations
The functions of Computable Analysis are defined by enhancing the capacities of normal Turing Machines to deal with real number inputs. We consider characterizations of these functions using function algebras, known as Real Recursive Functions. Bournez and Hainry 2006 [5] used a function algebra to characterize the twice continuously differentiable functions of Computable Analysis, restricted t...
متن کاملComputable Analysis of Differential Equations (Invited Talk)
In this talk, we discuss some algorithmic aspects of the local and global existence theory for various ordinary and partial differential equations. We will present a sample of results and give some idea of the motivation and general philosophy underlying these results.
متن کاملIndex sets for computable differential equations
dx = F (x, y) and the wave equation from the point of view of index sets. Index sets play an important role in the study of computable functions and computably enumerable sets (see, for example, Soare [21]) . Index sets for computable combinatorics have been studied by Gasarch and others [8, 9]; the latter paper provides a survey of such results. Index sets for Π1 classes were developed by the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1979
ISSN: 0003-4843
DOI: 10.1016/0003-4843(79)90021-4