Matches in SemOpenAlex for { <https://semopenalex.org/work/W2016162372> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W2016162372 endingPage "1250" @default.
- W2016162372 startingPage "1229" @default.
- W2016162372 abstract "For uniform meshes it is shown that any linear <italic>k</italic>-step formula can be formulated so that only <italic>k</italic> values need to be saved between steps. By saving additional <italic>m</italic> values it is possible to construct local polynomial approximations of degree <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k plus m minus 1> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>k + m - 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local monomial bases yield Nordsieck formulas. An explicit one-to-one correspondence is established between Nordsieck formulas and <italic>k</italic>-step formulas of order at least <italic>k</italic>, and a strong equivalence result is proved for all but certain pathological cases. Equivalence is also shown for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P left-parenthesis EC right-parenthesis Superscript asterisk> <mml:semantics> <mml:msup> <mml:mtext>P(EC)</mml:mtext> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>text {P(EC)}^ast</mml:annotation> </mml:semantics> </mml:math> </inline-formula> formulas but not for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P left-parenthesis EC right-parenthesis Superscript asterisk Baseline upper E> <mml:semantics> <mml:mrow> <mml:msup> <mml:mtext>P(EC)</mml:mtext> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:mtext>E</mml:mtext> </mml:mrow> <mml:annotation encoding=application/x-tex>text {P(EC)}^ast text {E}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> formulas." @default.
- W2016162372 created "2016-06-24" @default.
- W2016162372 creator A5049797937 @default.
- W2016162372 date "1979-01-01" @default.
- W2016162372 modified "2023-10-15" @default.
- W2016162372 title "Equivalent forms of multistep formulas" @default.
- W2016162372 cites W1964070472 @default.
- W2016162372 cites W1968576944 @default.
- W2016162372 cites W1971204352 @default.
- W2016162372 cites W1972848283 @default.
- W2016162372 cites W2040688117 @default.
- W2016162372 cites W2057948807 @default.
- W2016162372 cites W2154876043 @default.
- W2016162372 cites W2337935897 @default.
- W2016162372 cites W2529992474 @default.
- W2016162372 cites W4232398699 @default.
- W2016162372 cites W4239241337 @default.
- W2016162372 cites W4241430531 @default.
- W2016162372 cites W4252117010 @default.
- W2016162372 doi "https://doi.org/10.1090/s0025-5718-1979-0537967-4" @default.
- W2016162372 hasPublicationYear "1979" @default.
- W2016162372 type Work @default.
- W2016162372 sameAs 2016162372 @default.
- W2016162372 citedByCount "17" @default.
- W2016162372 countsByYear W20161623722012 @default.
- W2016162372 countsByYear W20161623722015 @default.
- W2016162372 countsByYear W20161623722016 @default.
- W2016162372 countsByYear W20161623722018 @default.
- W2016162372 countsByYear W20161623722021 @default.
- W2016162372 countsByYear W20161623722022 @default.
- W2016162372 crossrefType "journal-article" @default.
- W2016162372 hasAuthorship W2016162372A5049797937 @default.
- W2016162372 hasBestOaLocation W20161623721 @default.
- W2016162372 hasConcept C11413529 @default.
- W2016162372 hasConcept C18903297 @default.
- W2016162372 hasConcept C2777299769 @default.
- W2016162372 hasConcept C33923547 @default.
- W2016162372 hasConcept C86803240 @default.
- W2016162372 hasConceptScore W2016162372C11413529 @default.
- W2016162372 hasConceptScore W2016162372C18903297 @default.
- W2016162372 hasConceptScore W2016162372C2777299769 @default.
- W2016162372 hasConceptScore W2016162372C33923547 @default.
- W2016162372 hasConceptScore W2016162372C86803240 @default.
- W2016162372 hasIssue "148" @default.
- W2016162372 hasLocation W20161623721 @default.
- W2016162372 hasLocation W20161623722 @default.
- W2016162372 hasOpenAccess W2016162372 @default.
- W2016162372 hasPrimaryLocation W20161623721 @default.
- W2016162372 hasRelatedWork W1587224694 @default.
- W2016162372 hasRelatedWork W1979597421 @default.
- W2016162372 hasRelatedWork W2007980826 @default.
- W2016162372 hasRelatedWork W2061531152 @default.
- W2016162372 hasRelatedWork W2077600819 @default.
- W2016162372 hasRelatedWork W2142036596 @default.
- W2016162372 hasRelatedWork W2911598644 @default.
- W2016162372 hasRelatedWork W3002753104 @default.
- W2016162372 hasRelatedWork W4225152035 @default.
- W2016162372 hasRelatedWork W4245490552 @default.
- W2016162372 hasVolume "33" @default.
- W2016162372 isParatext "false" @default.
- W2016162372 isRetracted "false" @default.
- W2016162372 magId "2016162372" @default.
- W2016162372 workType "article" @default.