Matches in SemOpenAlex for { <https://semopenalex.org/work/W2076152001> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W2076152001 abstract "Abstract The paper deals with the approximate analysis of second order linear systems with variable coefficients through the application of orthogonal polynomials. The time-dependent functions appearing as coefficients in the system equations may be periodic, non-periodic or can have multiple turning points. These variable coefficients are replaced by simple functions, viz. a constant, a linear or a quadratic function, and orthogonal polynomial expansions are used in the desired time interval, such that the approximate differential equations thus obtained have known closed form solutions. In particular, expansions in ultraspherical polynomials have been treated in detail, which include the Chebyshev and Legendre polynomials as special cases. If the time-function is approximated by a constant, the approximate solutions are the sine and cosine functions, while a linear approximation leads to a solution in terms of Bessel functions of 1 3 order or Airy functions. The quadratic approximation of the function results in Weber's equations and the solutions are parabolic cylindrical functions. In the case of periodic coefficients, the functions are approximated such that the periods of the original and the approximate functions remain the same. The method has been applied to an equation with two turning points and to Mathieu's equation and the results are compared with numerical solutions. The well-known WKBJ results are also presented for comparison. Results obtained by the present approach agree with numerical solutions to a better accuracy depending on the choice of orthogonal polynomials used in the expansions. Moreover, in the case of turning point problems the approach is simpler as compared to other methods available in the literature and uniformly valid solutions are obtained without any difficulty." @default.
- W2076152001 created "2016-06-24" @default.
- W2076152001 creator A5001087538 @default.
- W2076152001 creator A5010297798 @default.
- W2076152001 date "1976-12-01" @default.
- W2076152001 modified "2023-09-27" @default.
- W2076152001 title "An approximate analysis of transient response of time-dependent linear systems by use of orthogonal polynomials" @default.
- W2076152001 cites W1981478126 @default.
- W2076152001 cites W1986760801 @default.
- W2076152001 cites W2001462365 @default.
- W2076152001 cites W2008095720 @default.
- W2076152001 cites W2009104615 @default.
- W2076152001 cites W2012653266 @default.
- W2076152001 cites W2014313209 @default.
- W2076152001 cites W2053092102 @default.
- W2076152001 cites W2059044701 @default.
- W2076152001 cites W2069786331 @default.
- W2076152001 cites W2074570511 @default.
- W2076152001 cites W2081338783 @default.
- W2076152001 cites W2082874925 @default.
- W2076152001 cites W2172255526 @default.
- W2076152001 cites W2295169085 @default.
- W2076152001 cites W2323855957 @default.
- W2076152001 cites W2563456453 @default.
- W2076152001 cites W3009787264 @default.
- W2076152001 cites W3038165843 @default.
- W2076152001 cites W363699219 @default.
- W2076152001 cites W561829213 @default.
- W2076152001 cites W592139942 @default.
- W2076152001 doi "https://doi.org/10.1016/0022-460x(76)90423-5" @default.
- W2076152001 hasPublicationYear "1976" @default.
- W2076152001 type Work @default.
- W2076152001 sameAs 2076152001 @default.
- W2076152001 citedByCount "10" @default.
- W2076152001 countsByYear W20761520012013 @default.
- W2076152001 countsByYear W20761520012016 @default.
- W2076152001 crossrefType "journal-article" @default.
- W2076152001 hasAuthorship W2076152001A5001087538 @default.
- W2076152001 hasAuthorship W2076152001A5010297798 @default.
- W2076152001 hasConcept C10628310 @default.
- W2076152001 hasConcept C107706756 @default.
- W2076152001 hasConcept C110342517 @default.
- W2076152001 hasConcept C111458787 @default.
- W2076152001 hasConcept C129785596 @default.
- W2076152001 hasConcept C134306372 @default.
- W2076152001 hasConcept C13982400 @default.
- W2076152001 hasConcept C178009071 @default.
- W2076152001 hasConcept C2524010 @default.
- W2076152001 hasConcept C28826006 @default.
- W2076152001 hasConcept C33923547 @default.
- W2076152001 hasConcept C48490523 @default.
- W2076152001 hasConcept C78045399 @default.
- W2076152001 hasConcept C90119067 @default.
- W2076152001 hasConceptScore W2076152001C10628310 @default.
- W2076152001 hasConceptScore W2076152001C107706756 @default.
- W2076152001 hasConceptScore W2076152001C110342517 @default.
- W2076152001 hasConceptScore W2076152001C111458787 @default.
- W2076152001 hasConceptScore W2076152001C129785596 @default.
- W2076152001 hasConceptScore W2076152001C134306372 @default.
- W2076152001 hasConceptScore W2076152001C13982400 @default.
- W2076152001 hasConceptScore W2076152001C178009071 @default.
- W2076152001 hasConceptScore W2076152001C2524010 @default.
- W2076152001 hasConceptScore W2076152001C28826006 @default.
- W2076152001 hasConceptScore W2076152001C33923547 @default.
- W2076152001 hasConceptScore W2076152001C48490523 @default.
- W2076152001 hasConceptScore W2076152001C78045399 @default.
- W2076152001 hasConceptScore W2076152001C90119067 @default.
- W2076152001 hasLocation W20761520011 @default.
- W2076152001 hasOpenAccess W2076152001 @default.
- W2076152001 hasPrimaryLocation W20761520011 @default.
- W2076152001 hasRelatedWork W1642531316 @default.
- W2076152001 hasRelatedWork W1927311801 @default.
- W2076152001 hasRelatedWork W1977827196 @default.
- W2076152001 hasRelatedWork W1979159302 @default.
- W2076152001 hasRelatedWork W2000612084 @default.
- W2076152001 hasRelatedWork W2001723278 @default.
- W2076152001 hasRelatedWork W2030325540 @default.
- W2076152001 hasRelatedWork W2080064889 @default.
- W2076152001 hasRelatedWork W2080643774 @default.
- W2076152001 hasRelatedWork W2086099792 @default.
- W2076152001 hasRelatedWork W2088537472 @default.
- W2076152001 hasRelatedWork W2108473871 @default.
- W2076152001 hasRelatedWork W2141344146 @default.
- W2076152001 hasRelatedWork W2169093037 @default.
- W2076152001 hasRelatedWork W2754533765 @default.
- W2076152001 hasRelatedWork W2755329187 @default.
- W2076152001 hasRelatedWork W3015121907 @default.
- W2076152001 hasRelatedWork W3132415942 @default.
- W2076152001 hasRelatedWork W3197209831 @default.
- W2076152001 hasRelatedWork W2524692928 @default.
- W2076152001 isParatext "false" @default.
- W2076152001 isRetracted "false" @default.
- W2076152001 magId "2076152001" @default.
- W2076152001 workType "article" @default.