{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,2]],"date-time":"2023-01-02T05:19:42Z","timestamp":1672636782282},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2020,3,31]]},"abstract":"\n We present a software package, M\n odes<\/jats:sc>\n , offering\n h<\/jats:italic>\n -adaptive and\n p<\/jats:italic>\n -adaptive linear multistep methods for first order initial value problems in ordinary differential equations. The implementation is based on a new parametric, grid-independent representation of multistep methods [Ar\u00e9valo and S\u00f6derlind 2017]. Parameters are supplied for over 60 methods. For nonstiff problems, all maximal order methods (\n p<\/jats:italic>\n =\n k<\/jats:italic>\n for explicit and\n p<\/jats:italic>\n =\n k<\/jats:italic>\n +1 for implicit methods) are supported. For stiff computation, implicit methods of order\n p<\/jats:italic>\n =\n k<\/jats:italic>\n are included.\n <\/jats:p>\n \n A collection of step-size controllers based on digital filters is provided, generating smooth step-size sequences offering improved computational stability. Controllers may be selected to match method and problem classes. A new system for automatic order control is also provided for designated families of multistep methods, offering simultaneous\n h<\/jats:italic>\n - and\n p<\/jats:italic>\n -adaptivity.\n <\/jats:p>\n \n Implemented as a M\n atlab<\/jats:sc>\n toolbox, the software covers high order computations with linear multistep methods within a unified, generic framework. Computational experiments show that the new software is competitive and offers qualitative improvements. M\n odes<\/jats:sc>\n is available for downloading and is primarily intended as a platform for developing a new generation of state-of-the-art multistep solvers, as well as for true\n ceteris paribus<\/jats:italic>\n evaluation of algorithmic components. This also enables\n method comparisons<\/jats:italic>\n within a single implementation environment.\n <\/jats:p>","DOI":"10.1145\/3372159","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T10:23:08Z","timestamp":1584699788000},"page":"1-17","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["A Software Platform for Adaptive High Order Multistep Methods"],"prefix":"10.1145","volume":"46","author":[{"given":"Carmen","family":"Ar\u00e9valo","sequence":"first","affiliation":[{"name":"Center for Mathematical Sciences, Lund Institute of Technology, Lund, Sweden"}]},{"given":"Erik","family":"Jonsson-Glans","sequence":"additional","affiliation":[{"name":"HiQ Ace AB, Link\u00f6ping, Lund, Sweden"}]},{"given":"Josefine","family":"Olander","sequence":"additional","affiliation":[{"name":"HiQ Ace AB, Link\u00f6ping, Lund, Sweden"}]},{"given":"Monica Selva","family":"Soto","sequence":"additional","affiliation":[{"name":"Department of Mathematical Engineering, University of Concepci\u00f3n, Chile"}]},{"given":"Gustaf","family":"S\u00f6derlind","sequence":"additional","affiliation":[{"name":"Center for Mathematical Sciences, Lund University, Lund, Sweden"}]}],"member":"320","published-online":{"date-parts":[[2020,3,20]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(01)00138-6"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.4208\/jcm.1611-m2015-0404"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"C. Ar\u00e9valo G. S\u00f6derlind Y. Hadjimichael and I. Fekete. 2019. Local error estimation and step size control in adaptive linear multistep methods. Accepted for publication in Numer. Algorithms. C. Ar\u00e9valo G. S\u00f6derlind Y. Hadjimichael and I. Fekete. 2019. Local error estimation and step size control in adaptive linear multistep methods. Accepted for publication in Numer. Algorithms.","DOI":"10.1007\/s11075-020-00900-1"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/0910062"},{"key":"e_1_2_1_5_1","volume-title":"Numerical Initial Value Problems in Ordinary Differential Equations","author":"Gear C. W."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287109"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1218052.1218054"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2012.03.014"},{"key":"e_1_2_1_9_1","unstructured":"F. Mazzia and C. Magherini. 2008. Test Set for Initial Value Problem Solvers Release 2.4. Technical Report. Department of Mathematics University of Bari Italy. archimede.dm.uniba.it\/∼testset\/testsetivpsolvers. F. Mazzia and C. Magherini. 2008. Test Set for Initial Value Problem Solvers Release 2.4. Technical Report. Department of Mathematics University of Bari Italy. archimede.dm.uniba.it\/∼testset\/testsetivpsolvers."},{"key":"e_1_2_1_10_1","first-page":"22","article-title":"On numerical integration of ordinary differential equations","volume":"16","author":"Nordsieck A.","year":"1962","journal-title":"MathComp"},{"key":"e_1_2_1_11_1","unstructured":"J. Olander and E. Jonsson-Glans. 2016. Construction and Benchmarking of Adaptive Parametrized Linear Multistep Methods. Master\u2019s Thesis. Lund Institute of Technology (LTH) Sweden. Order code: LUTFNA-3039-2016. J. Olander and E. Jonsson-Glans. 2016. Construction and Benchmarking of Adaptive Parametrized Linear Multistep Methods. Master\u2019s Thesis. Lund Institute of Technology (LTH) Sweden. Order code: LUTFNA-3039-2016."},{"key":"e_1_2_1_12_1","volume-title":"Proc. IMACS World Congress","author":"Petzold L.","year":"1982"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594276424"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/641876.641877"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.5555\/1642738.1642919"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-014-0503-3"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/1124467.1716868"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3372159","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T07:20:57Z","timestamp":1672557657000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3372159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,20]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3,31]]}},"alternative-id":["10.1145\/3372159"],"URL":"http:\/\/dx.doi.org\/10.1145\/3372159","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":["Applied Mathematics","Software"],"published":{"date-parts":[[2020,3,20]]},"assertion":[{"value":"2018-02-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-11-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-03-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}