@misc{LopezFernandezPalenciaSchaedle2005, author = {Lopez-Fernandez, Maria and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {A spectral order method for inverting sectorial Laplace transforms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8607}, number = {05-26}, year = {2005}, abstract = {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.}, language = {en} } @article{LopezFernandezLubichPalenciaetal.2005, author = {L{\´o}pez-Fern{\´a}ndez, Maria and Lubich, Christian and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {Fast Runge-Kutta approximation of inhomogeneous parabolic equations}, volume = {102}, journal = {Numer. Math.}, doi = {http://dx.doi.org/10.1007/s00211-005-0624-3}, pages = {277 -- 291}, year = {2005}, language = {en} } @article{LopezFernandezPalenciaSchaedle2006, author = {Lopez-Fernandez, Maria and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {A spectral order method for inverting sectorial Laplace transforms}, volume = {44}, journal = {SIAM J. Numer. Anal.}, number = {3}, doi = {/10.1137/050629653}, pages = {1332 -- 1350}, year = {2006}, language = {en} } @misc{LopezFernandezLubichPalenciaetal.2005, author = {Lopez-Fernandez, Maria and Lubich, Christian and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {Fast Runge-Kutta approximation of inhomogeneous parabolic equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8443}, number = {05-10}, year = {2005}, abstract = {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.}, language = {en} }