Opuscula Math. 27, no. 2 (2007), 205-220
Opuscula Mathematica
The use of integral information in the solution of a two-point boundary value problem
Abstract. We study the worst-case \(\varepsilon\)-complexity of a two-point boundary value problem \(u^{\prime\prime}(x)=f(x)u(x)\), \(x \in [0,T]\), \(u(0)=c\), \(u^{\prime}(T)=0\), where \(c,T \in \mathbb{R}\) (\(c \neq 0\), \(T \gt 0\)) and \(f\) is a nonnegative function with \(r\) (\(r\geq 0\)) continuous bounded derivatives. We prove an upper bound on the complexity for linear information showing that a speed-up by two orders of magnitude can be obtained compared to standard information. We define an algorithm based on integral information and analyze its error, which provides an upper bound on the \(\varepsilon\)-complexity.
Keywords: boundary value problem, complexity, worst case setting, linear information.
Mathematics Subject Classification: 68Q25, 65L10.
- Tomasz Drwięga
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
- Received: 2007-01-27.
