Complexity theory of real functions
Complexity theory of real functions
Computable analysis: an introduction
Computable analysis: an introduction
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Computing the solution of the Korteweg-de Vries equation with arbitrary precision on turing machines
Theoretical Computer Science
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We study the computability properties of symmetric hyperbolic systems of PDE's A@?u@?t+@?i=1mB"i@?u@?x"i=0, A=A^*0, B"i=B"i^*, with the initial condition u|"t"="0=@f(x"1,...,x"m). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A,B"1,...,B"m satisfying some natural conditions) any initial function @f@?C^k^+^1(Q,R^n), k=1, to the unique solution u@?C^k(H,R^n), where Q=[0,1]^m and H is the nonempty domain of correctness of the system.