Computational complexity of solving polynomial differential equations over unbounded domains
نویسندگان
چکیده
منابع مشابه
Computational complexity of solving polynomial differential equations over unbounded domains
In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) y′ = p(y) over unbounded time domains, where p is a vector of polynomials. Contrarily to the bounded (compact) time case, this problem has not been well-studied, apparently due to the “intuition” that it can always be reduced to the bounded case by using rescaling techniques. However, as ...
متن کاملComputational complexity of solving polynomial differential equations over unbounded domains with non-rational coefficients
In this note, we extend the result of [PG16] about the complexity of solving polynomial differential equations over unbounded domains to work with non-rational input. In order to deal with arbitrary input, we phrase the result in framework of Conputable Analysis [Ko91]. As a side result, we also get a uniform result about complexity of the operator, and not just about the solution. The complexi...
متن کاملSolving Analytic Differential Equations in Polynomial Time over Unbounded Domains
In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of R and C, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of definition, provided it satisfies a very generous bound on its growth, and that the...
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کاملSolving Linear Equations over Polynomial Semirings
We consider the problem of solving linear equations over various semirings. In particular, solving of linear equations over polynomial rings with the additional restriction that the solutions must have only non-negative coefficients is shown to be undecidable. Applications to undecidability proofs of several unification problems are illustrated, one of which, unification modulo one associative-...
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: Theoretical Computer Science
سال: 2016
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.02.002