Matches in SemOpenAlex for { <https://semopenalex.org/work/W3089386356> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W3089386356 abstract "The Euler–Maclaurin (EM) formulae relate sums and integrals. Discovered nearly 300 years ago, they have lost none of their importance over the years, and are nowadays routinely taught in scientific computing and numerical analysis courses. The two common versions can be viewed as providing error expansions for the trapezoidal rule and for the midpoint rule, respectively. More importantly, they provide a means for evaluating many infinite sums to high levels of accuracy. However, in all but the simplest cases, calculating very high-order derivatives analytically becomes prohibitively complicated. When approximating such derivatives with finite differences (FD), the choice of step size typically requires a severe trade-off between errors due to truncation and to rounding. We show here that, in the special case of EM expansions, FD approximations can provide excellent accuracy without the step size having to go to zero. While FD approximations of low-order derivatives to high orders of accuracy have many applications for solving ODEs and PDEs, the present context is unusual in that it relies on FD approximations to derivatives of very high orders. The application to infinite sums ensures that one can use centred FD formulae (which are not subject to the Runge phenomenon)." @default.
- W3089386356 created "2020-10-08" @default.
- W3089386356 creator A5029242127 @default.
- W3089386356 date "2020-09-01" @default.
- W3089386356 modified "2023-09-30" @default.
- W3089386356 title "Euler–Maclaurin expansions without analytic derivatives" @default.
- W3089386356 cites W1558122728 @default.
- W3089386356 cites W2001563191 @default.
- W3089386356 cites W2028033705 @default.
- W3089386356 cites W2030762303 @default.
- W3089386356 cites W2061269704 @default.
- W3089386356 cites W2068424476 @default.
- W3089386356 cites W2470050293 @default.
- W3089386356 cites W2797202806 @default.
- W3089386356 cites W2810056370 @default.
- W3089386356 cites W2886567865 @default.
- W3089386356 cites W3021154445 @default.
- W3089386356 cites W3045215878 @default.
- W3089386356 cites W3045327592 @default.
- W3089386356 cites W3100091305 @default.
- W3089386356 cites W4299550265 @default.
- W3089386356 cites W4379338011 @default.
- W3089386356 doi "https://doi.org/10.1098/rspa.2020.0441" @default.
- W3089386356 hasPublicationYear "2020" @default.
- W3089386356 type Work @default.
- W3089386356 sameAs 3089386356 @default.
- W3089386356 citedByCount "4" @default.
- W3089386356 countsByYear W30893863562020 @default.
- W3089386356 countsByYear W30893863562022 @default.
- W3089386356 countsByYear W30893863562023 @default.
- W3089386356 crossrefType "journal-article" @default.
- W3089386356 hasAuthorship W3089386356A5029242127 @default.
- W3089386356 hasBestOaLocation W30893863561 @default.
- W3089386356 hasConcept C10138342 @default.
- W3089386356 hasConcept C104942944 @default.
- W3089386356 hasConcept C105795698 @default.
- W3089386356 hasConcept C106195933 @default.
- W3089386356 hasConcept C111919701 @default.
- W3089386356 hasConcept C127349201 @default.
- W3089386356 hasConcept C134306372 @default.
- W3089386356 hasConcept C136625980 @default.
- W3089386356 hasConcept C151730666 @default.
- W3089386356 hasConcept C162324750 @default.
- W3089386356 hasConcept C182306322 @default.
- W3089386356 hasConcept C193386753 @default.
- W3089386356 hasConcept C2524010 @default.
- W3089386356 hasConcept C2779343474 @default.
- W3089386356 hasConcept C28826006 @default.
- W3089386356 hasConcept C33923547 @default.
- W3089386356 hasConcept C34130140 @default.
- W3089386356 hasConcept C34862557 @default.
- W3089386356 hasConcept C41008148 @default.
- W3089386356 hasConcept C62884695 @default.
- W3089386356 hasConcept C78727 @default.
- W3089386356 hasConcept C85807060 @default.
- W3089386356 hasConcept C86803240 @default.
- W3089386356 hasConceptScore W3089386356C10138342 @default.
- W3089386356 hasConceptScore W3089386356C104942944 @default.
- W3089386356 hasConceptScore W3089386356C105795698 @default.
- W3089386356 hasConceptScore W3089386356C106195933 @default.
- W3089386356 hasConceptScore W3089386356C111919701 @default.
- W3089386356 hasConceptScore W3089386356C127349201 @default.
- W3089386356 hasConceptScore W3089386356C134306372 @default.
- W3089386356 hasConceptScore W3089386356C136625980 @default.
- W3089386356 hasConceptScore W3089386356C151730666 @default.
- W3089386356 hasConceptScore W3089386356C162324750 @default.
- W3089386356 hasConceptScore W3089386356C182306322 @default.
- W3089386356 hasConceptScore W3089386356C193386753 @default.
- W3089386356 hasConceptScore W3089386356C2524010 @default.
- W3089386356 hasConceptScore W3089386356C2779343474 @default.
- W3089386356 hasConceptScore W3089386356C28826006 @default.
- W3089386356 hasConceptScore W3089386356C33923547 @default.
- W3089386356 hasConceptScore W3089386356C34130140 @default.
- W3089386356 hasConceptScore W3089386356C34862557 @default.
- W3089386356 hasConceptScore W3089386356C41008148 @default.
- W3089386356 hasConceptScore W3089386356C62884695 @default.
- W3089386356 hasConceptScore W3089386356C78727 @default.
- W3089386356 hasConceptScore W3089386356C85807060 @default.
- W3089386356 hasConceptScore W3089386356C86803240 @default.
- W3089386356 hasIssue "2241" @default.
- W3089386356 hasLocation W30893863561 @default.
- W3089386356 hasOpenAccess W3089386356 @default.
- W3089386356 hasPrimaryLocation W30893863561 @default.
- W3089386356 hasRelatedWork W2063840785 @default.
- W3089386356 hasRelatedWork W2330791370 @default.
- W3089386356 hasRelatedWork W2357395917 @default.
- W3089386356 hasRelatedWork W2370851183 @default.
- W3089386356 hasRelatedWork W2543612152 @default.
- W3089386356 hasRelatedWork W2606646591 @default.
- W3089386356 hasRelatedWork W3018722875 @default.
- W3089386356 hasRelatedWork W3089386356 @default.
- W3089386356 hasRelatedWork W4252588149 @default.
- W3089386356 hasRelatedWork W2342494873 @default.
- W3089386356 hasVolume "476" @default.
- W3089386356 isParatext "false" @default.
- W3089386356 isRetracted "false" @default.
- W3089386356 magId "3089386356" @default.
- W3089386356 workType "article" @default.