Trigonometrically-Fitted Methods: A Review
Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi came up with the idea of using information on the fr...
Saved in:
| Published in | Mathematics (Basel) Vol. 7; no. 12; p. 1197 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.12.2019
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math7121197 |
Cover
| Abstract | Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi came up with the idea of using information on the frequency of a solution to modify linear multistep methods by allowing the coefficients to depend on the frequency. Thus the methods integrate exactly appropriate trigonometric polynomials. This was done for both first order systems and second order initial value problems. Gautschi concluded that “the error reduction is not very substantial unless” the frequency estimate is close enough. As a result, no other work was done in this direction until 1984 when Neta and Ford showed that “Nyström’s and Milne-Simpson’s type methods for systems of first order initial value problems are not sensitive to changes in frequency”. This opened the flood gates and since then there have been many papers on the subject. |
|---|---|
| AbstractList | Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi came up with the idea of using information on the frequency of a solution to modify linear multistep methods by allowing the coefficients to depend on the frequency. Thus the methods integrate exactly appropriate trigonometric polynomials. This was done for both first order systems and second order initial value problems. Gautschi concluded that “the error reduction is not very substantial unless” the frequency estimate is close enough. As a result, no other work was done in this direction until 1984 when Neta and Ford showed that “Nyström’s and Milne-Simpson’s type methods for systems of first order initial value problems are not sensitive to changes in frequency”. This opened the flood gates and since then there have been many papers on the subject. |
| Author | Neta, Beny Chun, Changbum |
| Author_xml | – sequence: 1 givenname: Changbum surname: Chun fullname: Chun, Changbum – sequence: 2 givenname: Beny orcidid: 0000-0002-7417-7496 surname: Neta fullname: Neta, Beny |
| BookMark | eNqFj0FLAzEQhYNUsNae_AML3tTVTbJJNt5KsSpUBKnnZTabtSnbTU3Slv57U-qhiOBcZhi-mffeOep1ttMIXeLsjlKZ3S8hzAUmGEtxgvqEEJGKuO8dzWdo6P0iiyUxLXLZR9czZz5tZ5c6OKOgbXfpxISg6-RVh7mt_UMySt71xujtBTptoPV6-NMH6GPyOBs_p9O3p5fxaJoqIouQFoI0tQAtJRYsFxnDwJXaqwPoSleE5ZIC45zUvMo5BZ5TqUE1kNWMMEoH6Pbwd92tYLeNnsqVM0twuxJn5T5qeRQ14lcHfOXs11r7UC7s2nXRYRmlCs5wEVUG6OZAKWe9d7r55yf-RSsTIBjbBQem_fPmG4Q-cj4 |
| CitedBy_id | crossref_primary_10_3390_axioms13080514 crossref_primary_10_3390_math12040504 crossref_primary_10_3390_sym16050508 crossref_primary_10_3390_math12233652 crossref_primary_10_3390_math9080806 crossref_primary_10_3390_math7121197 crossref_primary_10_3390_axioms13090649 |
| Cites_doi | 10.1017/S0305004100034526 10.1214/aoms/1177729955 10.1093/imamat/18.2.189 10.1016/0377-0427(86)90028-2 10.1086/115629 10.1016/0168-9274(86)90016-4 10.1016/j.cpc.2008.07.013 10.3390/math7121197 10.1016/j.cam.2005.03.035 10.1016/0377-0427(86)90033-6 10.1002/zamm.19620420906 10.1016/0010-4655(78)90047-4 10.1007/BF01952791 10.1080/00207169108803985 10.1137/S0036142995286763 10.1098/rspa.1993.0061 10.1137/0724041 10.1007/BF01386037 10.1093/imanum/7.4.407 10.1016/j.cam.2009.08.103 10.1007/s11075-007-9084-4 10.1016/j.cam.2005.04.044 10.1016/j.camwa.2005.11.041 10.2307/2002545 10.1016/0377-0427(92)90224-L 10.1098/rspa.2003.1210 10.1093/imanum/drl040 10.2307/2008328 10.1016/S0898-1221(03)80005-6 10.1142/S0129183101002292 10.1007/BF03546251 10.1007/BF01601084 10.1016/j.apnum.2008.03.018 10.1007/BF02163234 10.1007/BF01934522 10.1016/0377-0427(84)90066-9 10.1002/nme.1620150506 10.1016/S0010-4655(01)00285-5 10.1016/j.cpc.2007.07.007 10.1016/j.cam.2014.09.008 10.1007/BF02247883 10.1007/BF01937488 10.1080/00207168608803532 10.2514/6.1998-4577 |
| ContentType | Journal Article |
| Copyright | 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U ADTOC UNPAY |
| DOI | 10.3390/math7121197 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Advanced Technologies & Aerospace Database ProQuest Central Essentials ProQuest Central Technology Collection (via ProQuest SciTech Premium Collection) ProQuest One Community College ProQuest Central Engineering Research Database ProQuest Central Student SciTech Premium Collection (via ProQuest) ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database (Proquest) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository – sequence: 2 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2227-7390 |
| ExternalDocumentID | 10.3390/math7121197 10_3390_math7121197 |
| GroupedDBID | -~X 5VS 85S 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ABPPZ ABUWG ACIPV ACIWK ADBBV AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO GNUQQ GROUPED_DOAJ HCIFZ IAO K6V K7- KQ8 L6V M7S MODMG M~E OK1 PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC PTHSS RNS 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D M0N P62 PKEHL PQEST PQUKI PRINS Q9U ADTOC IPNFZ ITC RIG UNPAY |
| ID | FETCH-LOGICAL-c298t-872fd7ae9917547051a6cc7390aaebeb25493a5662d6b463a6439eacfa0d52533 |
| IEDL.DBID | UNPAY |
| ISSN | 2227-7390 |
| IngestDate | Sun Oct 26 04:16:48 EDT 2025 Fri Jul 25 12:10:00 EDT 2025 Thu Oct 16 04:28:33 EDT 2025 Thu Apr 24 23:14:53 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 12 |
| Language | English |
| License | cc-by |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c298t-872fd7ae9917547051a6cc7390aaebeb25493a5662d6b463a6439eacfa0d52533 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-7417-7496 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://www.mdpi.com/2227-7390/7/12/1197/pdf?version=1576219730 |
| PQID | 2548651846 |
| PQPubID | 2032364 |
| ParticipantIDs | unpaywall_primary_10_3390_math7121197 proquest_journals_2548651846 crossref_primary_10_3390_math7121197 crossref_citationtrail_10_3390_math7121197 |
| PublicationCentury | 2000 |
| PublicationDate | 2019-12-01 |
| PublicationDateYYYYMMDD | 2019-12-01 |
| PublicationDate_xml | – month: 12 year: 2019 text: 2019-12-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Mathematics (Basel) |
| PublicationYear | 2019 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Lambert (ref_17) 1962; 13 Wang (ref_42) 2005; 461 Lambert (ref_5) 1976; 18 Neta (ref_34) 2002; 50 (ref_50) 2009; 233 Twizell (ref_9) 1986; 15 ref_51 Ramos (ref_21) 2007; 27 Simos (ref_41) 1993; 441 Demba (ref_49) 2016; 109 Sommeijer (ref_27) 1987; 7 Chawla (ref_46) 1984; 24 Franco (ref_20) 2016; 273 (ref_35) 1998; 35 Obrechkoff (ref_15) 1942; 65 Sommeijer (ref_39) 1986; 2 Neta (ref_43) 2007; 54 Simos (ref_52) 2004; 460 Simos (ref_13) 1990; 45 Simos (ref_14) 2001; 12 (ref_19) 2007; 44 Simos (ref_11) 1991; 39 Brock (ref_23) 1952; 6 Tsitouras (ref_47) 2003; 45 Ramos (ref_26) 2015; 277 Franco (ref_45) 2006; 187 Gautschi (ref_1) 1961; 3 Salzer (ref_25) 1962; 42 Stiefel (ref_30) 1969; 13 Ananthakrishnaiah (ref_18) 1987; 49 ref_31 Achar (ref_16) 2011; 218 Greenwood (ref_22) 1949; 20 Ramos (ref_36) 2008; 178 Fang (ref_48) 2008; 179 Brusa (ref_6) 1980; 15 Neta (ref_28) 1989; 31 Neta (ref_38) 1986; 20 Thomas (ref_8) 1984; 24 Raptis (ref_29) 1978; 14 (ref_44) 2009; 59 Sommeijer (ref_7) 1987; 24 Simos (ref_33) 2001; 140 ref_40 ref_3 (ref_37) 2006; 192 Neta (ref_2) 1984; 10 Raptis (ref_10) 1991; 31 Dennis (ref_24) 1960; 56 Quinlan (ref_32) 1990; 100 Simos (ref_12) 1992; 39 Chawla (ref_4) 1986; 15 |
| References_xml | – volume: 56 start-page: 240 year: 1960 ident: ref_24 article-title: The numerical integration of ordinary differential equations possessing exponential type solutions publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004100034526 – volume: 109 start-page: 207 year: 2016 ident: ref_49 article-title: New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems publication-title: Int. J. Pure Appl. Math. – volume: 20 start-page: 608 year: 1949 ident: ref_22 article-title: Numerical integration of linear sums of exponential functions publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177729955 – volume: 18 start-page: 189 year: 1976 ident: ref_5 article-title: Symmetric multistep methods for periodic initial value problems publication-title: J. Inst. Math. Appl. doi: 10.1093/imamat/18.2.189 – volume: 15 start-page: 213 year: 1986 ident: ref_4 article-title: Families of two-step fourth order P-stable methods for second order differential equations publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(86)90028-2 – volume: 100 start-page: 1694 year: 1990 ident: ref_32 article-title: Symmetric multistep methods for the numerical integration of planetary orbits publication-title: Astronom. J. doi: 10.1086/115629 – volume: 2 start-page: 69 year: 1986 ident: ref_39 article-title: Symmetric linear multistep methods for second-order differential equations with periodic solutions publication-title: Appl. Numer. Math. doi: 10.1016/0168-9274(86)90016-4 – volume: 179 start-page: 801 year: 2008 ident: ref_48 article-title: Trigonometrically fitted explicit Numerov-type method for periodic IVPs with two frequencies publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2008.07.013 – ident: ref_51 doi: 10.3390/math7121197 – volume: 187 start-page: 41 year: 2006 ident: ref_45 article-title: A class of explicit two-step hybrid methods for second-order IVPs publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2005.03.035 – volume: 15 start-page: 261 year: 1986 ident: ref_9 article-title: Phase-lag analysis for a family of two-step methods for second order periodic initial value problems publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(86)90033-6 – volume: 42 start-page: 403 year: 1962 ident: ref_25 article-title: Trigonometric interpolation and predictor-corrector formulas for numerical integration publication-title: ZAMM doi: 10.1002/zamm.19620420906 – volume: 14 start-page: 1 year: 1978 ident: ref_29 article-title: Exponential-fitting methods for the numerical solution of the Schrödinger equation publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(78)90047-4 – volume: 31 start-page: 160 year: 1991 ident: ref_10 article-title: A four-step phase-fitted method for the numerical integration of second order initial-value problems publication-title: BIT doi: 10.1007/BF01952791 – volume: 39 start-page: 135 year: 1991 ident: ref_11 article-title: A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-value problem publication-title: Int. J. Comput. Math. doi: 10.1080/00207169108803985 – ident: ref_31 – volume: 35 start-page: 1684 year: 1998 ident: ref_35 article-title: A general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142995286763 – volume: 441 start-page: 283 year: 1993 ident: ref_41 article-title: A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial-value problems publication-title: Proc. R. Soc. Lond. A doi: 10.1098/rspa.1993.0061 – volume: 24 start-page: 595 year: 1987 ident: ref_7 article-title: Explicit Runge-Kutta-Nyström methods with reduced phase errors for computing oscillating solutions publication-title: SIAM J. Numer. Anal. doi: 10.1137/0724041 – volume: 3 start-page: 381 year: 1961 ident: ref_1 article-title: Numerical integration of ordinary differential equations based on trigonometric polynomials publication-title: Numer. Math. doi: 10.1007/BF01386037 – volume: 7 start-page: 407 year: 1987 ident: ref_27 article-title: Predictor-corrector methods for periodic second-order initial-value problems publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/7.4.407 – volume: 233 start-page: 969 year: 2009 ident: ref_50 article-title: Trigonometric polynomial or exponential fitting approach? publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.08.103 – volume: 44 start-page: 115 year: 2007 ident: ref_19 article-title: P-stable Obrechkoff methods of arbitrary order for second-order differential equations publication-title: Numer. Algor. doi: 10.1007/s11075-007-9084-4 – volume: 65 start-page: 191 year: 1942 ident: ref_15 article-title: On mechanical quadrature (Bulgarian, French summary) publication-title: Spis. Bulgar. Akad. Nauk – volume: 192 start-page: 100 year: 2006 ident: ref_37 article-title: Exponential fitting BDF algorithms: Explicit and implicit 0-stable methods publication-title: J. Comput. Math. Anal. doi: 10.1016/j.cam.2005.04.044 – volume: 54 start-page: 117 year: 2007 ident: ref_43 article-title: P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2005.11.041 – volume: 218 start-page: 2237 year: 2011 ident: ref_16 article-title: Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations publication-title: Appl. Math. Comput. – volume: 6 start-page: 63 year: 1952 ident: ref_23 article-title: The use of exponential sums in step by step integration publication-title: Math. Tables Aids Comput. doi: 10.2307/2002545 – volume: 39 start-page: 89 year: 1992 ident: ref_12 article-title: Explicit two-step methods with minimal phase-lag for the numerical integration of special second-order initial-value problems and their application to the one-dimensional Schrödinger equation publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(92)90224-L – volume: 273 start-page: 493 year: 2016 ident: ref_20 article-title: Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs publication-title: Appl. Math. Comput. – volume: 460 start-page: 561 year: 2004 ident: ref_52 article-title: Controlling the error growth in long-term numerical integration of perturbed oscillations in one or several frequencies publication-title: Proc. Math. Phys. Eng. Sci. doi: 10.1098/rspa.2003.1210 – volume: 27 start-page: 798 year: 2007 ident: ref_21 article-title: A family of A-stable Runge-Kutta collocation methods of higher order for initial value problems publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drl040 – volume: 49 start-page: 553 year: 1987 ident: ref_18 article-title: P-stable Obrechkoff methods with minimal phase-lag for periodic initial-value problems publication-title: Math. Comput. doi: 10.2307/2008328 – volume: 31 start-page: 161 year: 1989 ident: ref_28 article-title: Special methods for problems whose oscillatory solution is damped publication-title: Appl. Math. Comput. – volume: 45 start-page: 37 year: 2003 ident: ref_47 article-title: Explicit Numerov type methods with reduced number of stages publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(03)80005-6 – ident: ref_3 – volume: 12 start-page: 1035 year: 2001 ident: ref_14 article-title: A symmetric high order method with minimal phase-lag for the numerical solution of the Schrödinger equation publication-title: Int. J. Mod. Phys. C doi: 10.1142/S0129183101002292 – volume: 50 start-page: 255 year: 2002 ident: ref_34 article-title: A New Scheme for Trajectory Propagation publication-title: J. Astro. Sci. doi: 10.1007/BF03546251 – volume: 461 start-page: 1639 year: 2005 ident: ref_42 article-title: An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems publication-title: Proc. Math. Phys. Eng. Sci. – volume: 13 start-page: 223 year: 1962 ident: ref_17 article-title: On the solution of y’ = f(x,y) by a class of high accuracy difference formulae of low order publication-title: Z. Angew. Math. Phys. doi: 10.1007/BF01601084 – volume: 59 start-page: 815 year: 2009 ident: ref_44 article-title: Exponentially-fitted Obrechkoff methods for second-order differential equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2008.03.018 – volume: 13 start-page: 154 year: 1969 ident: ref_30 article-title: Stabilization of Cowell’s methods publication-title: Numer. Math. doi: 10.1007/BF02163234 – volume: 24 start-page: 117 year: 1984 ident: ref_46 article-title: Numerov made explicit has better stability publication-title: BIT doi: 10.1007/BF01934522 – volume: 10 start-page: 33 year: 1984 ident: ref_2 article-title: Families of methods for ordinary differential equations based on trigonometric polynomials publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(84)90066-9 – volume: 15 start-page: 685 year: 1980 ident: ref_6 article-title: A one-step method for the direct integration of structural dynamic equations publication-title: Internat. J. Numer. Meth. Engng. doi: 10.1002/nme.1620150506 – volume: 140 start-page: 358 year: 2001 ident: ref_33 article-title: An exponentially-fitted high order method for long-term integration of periodic initial-value problems publication-title: Comput. Phys. Comm. doi: 10.1016/S0010-4655(01)00285-5 – volume: 178 start-page: 15 year: 2008 ident: ref_36 article-title: Exponential fitting BDF-Runge-Kutta algorithms publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2007.07.007 – volume: 277 start-page: 94 year: 2015 ident: ref_26 article-title: On the choice of the frequency in trigonometrically-fitted methods for periodic problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2014.09.008 – volume: 45 start-page: 175 year: 1990 ident: ref_13 article-title: Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation publication-title: Computing doi: 10.1007/BF02247883 – volume: 24 start-page: 225 year: 1984 ident: ref_8 article-title: Phase properties of high order, almost P-stable formulae publication-title: BIT doi: 10.1007/BF01937488 – volume: 20 start-page: 67 year: 1986 ident: ref_38 article-title: Families of Backward Differentiation Methods based on Trigonometric Polynomials publication-title: Int. J. Comput. Math. doi: 10.1080/00207168608803532 – ident: ref_40 doi: 10.2514/6.1998-4577 |
| SSID | ssj0000913849 |
| Score | 2.134273 |
| SecondaryResourceType | review_article |
| Snippet | Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested... |
| SourceID | unpaywall proquest crossref |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database |
| StartPage | 1197 |
| SubjectTerms | Algebra Boundary value problems Differential equations Error reduction Floodgates Interpolation Mathematics Methods Numerical methods Ordinary differential equations Polynomials |
| SummonAdditionalLinks | – databaseName: ProQuest Central dbid: BENPR link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LS8NAEB5qelAP4hOrVXLQS2FpN69NBJEqDUVoEWmht7CPFIWQVpsi_ffO5tFWkN6XZfkmmflmH98HcCcVRxpCFcHiaxOHCkGE7DAy5Y4ub66UxQXZodcfO68Td1KDYfUWRl-rrHJinqjVTOo98jY2Mr7nYj_iPc2_iHaN0qerlYUGL60V1GMuMbYHdUsrYxlQf-4N397Xuy5aBdN3guKhno39fht54QfLdc7Y39K04Zv7y3TOVz88SbZKT3gMRyVnNLtFkE-gFqencDhYC64uzqA1wqXq9wnaIAthT1Yk_MyQTZqD3CJ68WB2zeIc4BzGYW_00ielDQKRVuBnmK-sqWI8RibHXIfhX8Q9KRkunnMMgdAtns2RllnKE4gw1yQD8-mUd5RrIZ27ACOdpfElmEJR4dvYMooAR7I4oC7rcEFjJqktAtqAVoVAJEuNcG1VkUTYK2i4oi24GhjpavC8kMb4f1izgjIq_49FtIlmA-7X8O6a5mr3NNdwgFQmKC6aNMHIvpfxDdKFTNyW38AvIYm-2A priority: 102 providerName: ProQuest |
| Title | Trigonometrically-Fitted Methods: A Review |
| URI | https://www.proquest.com/docview/2548651846 https://www.mdpi.com/2227-7390/7/12/1197/pdf?version=1576219730 |
| UnpaywallVersion | publishedVersion |
| Volume | 7 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAFT databaseName: Open Access Digital Library customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: KQ8 dateStart: 20130101 isFulltext: true titleUrlDefault: http://grweb.coalliance.org/oadl/oadl.html providerName: Colorado Alliance of Research Libraries – providerCode: PRVAON databaseName: Directory of Open Access Journals (DOAJ) customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVEBS databaseName: EBSCOhost Academic Search Ultimate customDbUrl: https://search.ebscohost.com/login.aspx?authtype=ip,shib&custid=s3936755&profile=ehost&defaultdb=asn eissn: 2227-7390 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: ABDBF dateStart: 20170101 isFulltext: true titleUrlDefault: https://search.ebscohost.com/direct.asp?db=asn providerName: EBSCOhost – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - trial do 30.11.2025 customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: AMVHM dateStart: 20170101 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources (selected full-text only) customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: http://www.proquest.com/pqcentral?accountid=15518 eissn: 2227-7390 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: BENPR dateStart: 20130301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Technology Collection customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: 8FG dateStart: 20130301 isFulltext: true titleUrlDefault: https://search.proquest.com/technologycollection1 providerName: ProQuest |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT8JAEJ0IHNSD30YUmx70QrJAW9qlXgwaKjGBEAMJnurutkRiU4ktGvz1zvYD0Rhj4n3a7PbN7rzXnZ0BOBMeQxqieQSDr0GaGueEiwYlE9aU4c0UIk2Q7VvdUfN2bI6zPqdRllaJUnyabNLyniahqMrrtK7pdXniVZ95k8vX7FeShmQZVxw6aQFKlolkvAilUX_Qvpct5fKH01t5hnwNksBHmhQ1o1_j0Ce5XJ-HM7Z4Y0GwEmecbXjIR5imlzzV5jGvifdvxRv_MYUd2Mo4qNpOnWYX1vxwDzZ7ywKu0T5Uh6ja5X0H2XALYQwWxJnGyE7VXtJyOrpQ22p6rnAAI6czvO6SrK0CEbrdinH_0yceZT4yQ2o2Ka5KZgkhx8gYQsqlZDQY0jzdszgixiRpwf15whqeqSM9PIRi-Bz6R6ByT-MtAyUot9GS-jZOp8G45lOhGdzWylDNP7IrsprjsvVF4KL2kIi4K4iU0XNy41laauNns0qOlputt8jFMbcsE9WqVYbzJYK_veb4j3YnsIEcyU4zWCpQjF_m_inykJgrUGg5NwqUrjr9wZ2SqHkl878P9onZ8Q |
| linkProvider | Unpaywall |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LTwIxEG4IHNCD8RlR1D3IhaSBfXZrQgwqBOQRYyDhtrbdJZpsFnSXEP6cv83pPgAT441706RfpzPf13ZmELoVLgMaoroYgq-ODZVzzEWd4CkzZHgzhUg-yA6tzth4npiTHPrOcmHkt8rMJ8aO2p0JeUdeAyFjWyboEet-_oll1yj5upq10GBpawW3EZcYSxM7et5qCRIubHSfYL8rmtZujR47OO0ygIVG7QjcgTZ1CfOAKBHTIGCkzBKC6LTOGKyQSwWlM2A9mmtxWACTMRzc1ZTVXVMz5YUohICCoRsUxF_hoTV8eV3f8siqm7ZBk8RAHeasAQ99J3FdNfI7FG74bXERzNlqyXx_K9S1D9FBylGVZmJURyjnBcdof7Au8BqeoOoIoJH5ELIhF2yzv8LtjwjYqzKIW1KHd0pTSd4dTtF4J4CcoXwwC7xzpHBX5bYOEpVTGEk8qpqkzrjqEaHqnKolVM0QcERak1y2xvAd0CYSLmcLrhJYVjZ4npTi-HtYOYPSSc9j6Gysp4Qqa3j_m-bi_2luULEzGvSdfnfYu0R7QKNo8smljPLR18K7AqoS8evUHhT0tmsT_AFCBvtG |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LS8NAEB5KBR8H8YnVqjnYSyG0eW4iiBRrbK0tHlroLe5uEhRCWk1K6V_z1zmbR1tBvPW-LMm3X2a-2cwD4IZ7FGWI4snofDVZVxiTGW8SOaC6cG8G51mC7MDsjPTnsTEuwXdRCyPSKgubmBpqb8LFHXkDAxnLNDAeMRtBnhbx2nbup5-ymCAl_rQW4zQyivT8xRzDt_iu28azrqmq8zh86Mj5hAGZq7aVoClQA49QH0USMXSCBKUm50Szm5Ti2zERPWkUFY_qmQwfngr_jaYqoE3PUA1xGYrmf4uILu6iSt15Wt7viH6blm5nJYEa7thABfpO0o5q5LcTXCnbnVk0pYs5DcM1J-ccwH6uTqVWRqdDKPnREez1l61d42OoDxEIUQkhRnHhAYcL2flIULdK_XQYdXwrtaTsj8MJjDYCxymUo0nkn4HEPIVZGganzMaVxLcVgzQpU3zCFY3ZSgXqBQIuz7uRi6EYoYtRiYDLXYOrgpwqFk-zJhx_L6sWULr5lxi7K95UoLaE979tzv_f5hq2kXjuS3fQu4Bd1E92lt1ShXLyNfMvUaMk7ColgwRvm2bfD2H4-OA |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NS8NAEB20PagHv8VqlRz0UljTzdc2XqSIpQgtHlqop7i7SbAYYjGpUn-9s82mVhERvE_Cbt7sznvZ2RmAMxlypCE0JBh8beJQIYiQTUZi7qjw5kpZJMj2ve7QuR25I93nNNNplSjFx_NNWt3TJAxVuclMapnqxMuchPHVq_6VRJEs44pDJ12FquciGa9Addi_a9-rlnLlw8WtPFu9BkngI5sXNWNf49AnuVybphM-e-NJshRnOlvwUI6wSC95upjm4kK-fyve-I8pbMOm5qBGu3CaHViJ0l3Y6C0KuGZ70Bigalf3HVTDLYQxmZHOOEd2avTmLaezS6NtFOcK-zDs3Ayuu0S3VSDS8ls57n9WHDIeITNkrsNwVXJPSjVGzhFSoSSjzZHmWaEnEDGuSAvuzzFvhq6F9PAAKulzGh2CIUIqWjZKUOGjJYt8nE6TCxoxSW3h0xo0yo8cSF1zXLW-SALUHgqRYAmRGnpOaTwpSm38bFYv0Qr0essCHHPLc1GtejU4XyD422uO_mh3DOvIkfwig6UOlfxlGp0gD8nFqfa1Dxnj1nw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Trigonometrically-Fitted+Methods%3A+A+Review&rft.jtitle=Mathematics+%28Basel%29&rft.au=Chun%2C+Changbum&rft.au=Neta%2C+Beny&rft.date=2019-12-01&rft.issn=2227-7390&rft.eissn=2227-7390&rft.volume=7&rft.issue=12&rft.spage=1197&rft_id=info:doi/10.3390%2Fmath7121197&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_math7121197 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2227-7390&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2227-7390&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2227-7390&client=summon |