TY  - JOUR
ID  - Drwięga2007
LB  - Drwięga2007
AU  - Drwięga, Tomasz
TI  - The use of integral information in the solution of a two-point boundary value problem
ST  - The use of integral information in the solution of a two-point boundary value problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2007
VL  - 27
IS  - 2
SP  - 205
EP  - 220
DO  - http://dx.doi.org/10.7494/OpMath.2007.27.2.205
UR  - http://dx.doi.org/10.7494/OpMath.2007.27.2.205
AB  - 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.
KW  - boundary value problem
KW  - complexity
KW  - worst case setting
KW  - linear information
SN  - 1232-9274
ER  -