{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:06:29Z","timestamp":1751871989271,"version":"3.38.0"},"reference-count":26,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[1996,3,1]],"date-time":"1996-03-01T00:00:00Z","timestamp":825638400000},"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 Supercomputer Applications and High Performance Computing"],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:p> We investigate different parallel algorithms for the iter ated Runge-Kutta method on distributed memory mul tiprocessors for the solution of systems of ordinary differential equations (ODEs). The iterated Runge-Kutta method is an iteration scheme for the numerical solu tion of initial-value problems of nonstiff ODEs; embed ded approximation formulae are used to control the step size. The parallel algorithms realize potential par allelism across the method and the system in a group- SPMD (single-program, multiple-data) programming style, using an appropriate set of communication prim itives that can be implemented on all common topolo gies. A theoretical performance analysis with run-time formulae and a run-time simulation show the value of the algorithms. The implementation on the Intel iPSC\/ 860 confirms the predicted run times. The speedup values depend strongly on the particular system of ODEs to be solved. The parallel iterated Runge-Kutta method is applied to a typical discretization problem, the discretized Brusselator equation. Application-spe cific modifications of the general parallel ODE solver are developed, which result in a considerable reduc tion in the parallel execution time. <\/jats:p>","DOI":"10.1177\/109434209601000103","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T01:17:47Z","timestamp":1173057467000},"page":"62-90","source":"Crossref","is-referenced-by-count":17,"title":["Parallel Implementations of Iterated Runge-Kutta Methods"],"prefix":"10.1177","volume":"10","author":[{"given":"Thomas","family":"Rauber","sequence":"first","affiliation":[{"name":"COMPUTER SCIENCE DEPARTMENT UNIVERSIT\u00c4T DES SAARLANDES\rSAARBR\u00dcCKEN, GERMANY"}]},{"given":"Gudula","family":"R\u00fcnger","sequence":"additional","affiliation":[{"name":"COMPUTER SCIENCE DEPARTMENT UNIVERSIT\u00c4T DES SAARLANDES\rSAARBR\u00dcCKEN, GERMANY"}]}],"member":"179","published-online":{"date-parts":[[1996,3,1]]},"reference":[{"key":"atypb1","first-page":"277","volume":"31","author":"Bellen, A.","year":"1990","journal-title":"Appl. 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