{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:54:55Z","timestamp":1777676095803,"version":"3.51.4"},"reference-count":10,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[1999,11,1]],"date-time":"1999-11-01T00:00:00Z","timestamp":941414400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[1999,11]]},"abstract":"<jats:p>PVODE is a general-purpose solver for ordinary differential equation (ODE) systems that implements methods for both stiff and nonstiff systems. The code is designed for single-program multiple-data environments. It is written in ANSI standard C, with a highly modular structure. The version being distributed uses the message-passing interface (MPI) system for communication. In the stiff case, PVODE uses a backward differentiation formula method combined with preconditioned GMRES iteration. Parallelism is achieved by distributing the ODE solution vector into user-specified segments and parallelizing a set of vector kernels accordingly. For PDE-based ODE systems, we provide a module that generates a band block-diagonal preconditioner for use with the GMRES iteration. We also provide a set of interfaces to accommodate Fortran applications. The paper includes a stiff example problem and test results on a Cray-T3D with three different message-passing systems. PVODE is publicly available.<\/jats:p>","DOI":"10.1177\/109434209901300405","type":"journal-article","created":{"date-parts":[[2005,3,8]],"date-time":"2005-03-08T14:23:33Z","timestamp":1110291813000},"page":"354-365","source":"Crossref","is-referenced-by-count":71,"title":["PVODE, an ODE Solver for Parallel Computers"],"prefix":"10.1177","volume":"13","author":[{"given":"George D.","family":"Byrne","sequence":"first","affiliation":[{"name":"Applied Mathematics Department and Chemical & Environmental Engineering Department, Illinois Institute of Technology, Chicago, IL, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan C.","family":"Hindmarsh","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National\r                        Laboratory, Livermore, CA, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1999,11,1]]},"reference":[{"key":"atypb1","volume-title":"PETSc 2.0 users manual","author":"Balay, S.","year":"1996"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/0910062"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(89)90110-0"},{"key":"atypb4","first-page":"323","volume-title":"Computational ordinary differential equations","author":"Byrne, G. D.","year":"1992"},{"key":"atypb5","volume-title":"User documentation for PVODE, an ODE solver for parallel computers","author":"Byrne, G. D.","year":"1998"},{"key":"atypb6","volume-title":"CVODE user guide","author":"Cohen, S. D.","year":"1994"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1063\/1.4822377"},{"key":"atypb8","volume-title":"Using MPI: Port -able parallel programming with the message-passing inter-face","author":"Gropp, W.","year":"1994"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.2172\/304578"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.2172\/420379"}],"container-title":["The International Journal of High Performance Computing Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/109434209901300405","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/109434209901300405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T08:17:39Z","timestamp":1777450659000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/109434209901300405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,11]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,11]]}},"alternative-id":["10.1177\/109434209901300405"],"URL":"https:\/\/doi.org\/10.1177\/109434209901300405","relation":{},"ISSN":["1094-3420","1741-2846"],"issn-type":[{"value":"1094-3420","type":"print"},{"value":"1741-2846","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,11]]}}}