TY - GEN A1 - Lopez-Fernandez, Maria A1 - Palencia, Cesar A1 - Schädle, Achim T1 - A spectral order method for inverting sectorial Laplace transforms N2 - Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is proposed. The method takes into account the available information about the errors arising in the evaluations. Several numerical illustrations are provided. T3 - ZIB-Report - 05-26 KW - Laplace transform KW - numerical inversion KW - parabolic KW - spectral order KW - parallelizable Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8607 ER - TY - JOUR A1 - López-Fernández, Maria A1 - Lubich, Christian A1 - Palencia, Cesar A1 - Schädle, Achim T1 - Fast Runge-Kutta approximation of inhomogeneous parabolic equations JF - Numer. Math. Y1 - 2005 U6 - https://doi.org/http://dx.doi.org/10.1007/s00211-005-0624-3 VL - 102 SP - 277 EP - 291 ER - TY - JOUR A1 - Lopez-Fernandez, Maria A1 - Palencia, Cesar A1 - Schädle, Achim T1 - A spectral order method for inverting sectorial Laplace transforms JF - SIAM J. Numer. Anal. Y1 - 2006 U6 - https://doi.org//10.1137/050629653 VL - 44 IS - 3 SP - 1332 EP - 1350 ER - TY - GEN A1 - Lopez-Fernandez, Maria A1 - Lubich, Christian A1 - Palencia, Cesar A1 - Schädle, Achim T1 - Fast Runge-Kutta approximation of inhomogeneous parabolic equations N2 - The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\varepsilon$, by solving only $$O\Big(\log N\, \log \frac1\varepsilon \Big) $$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm. T3 - ZIB-Report - 05-10 KW - parabolic equation KW - Runge-Kutta methods Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8443 ER -