{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:04:12Z","timestamp":1649203452500},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[1983,12,1]],"date-time":"1983-12-01T00:00:00Z","timestamp":439084800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1983,12]]},"DOI":"10.1007\/bf02251239","type":"journal-article","created":{"date-parts":[[2005,11,15]],"date-time":"2005-11-15T11:28:32Z","timestamp":1132054112000},"page":"371-381","source":"Crossref","is-referenced-by-count":0,"title":["Nonlinear contractivity of a class of semi-implicit multistep methods"],"prefix":"10.1007","volume":"31","author":[{"given":"K.","family":"Strehmel","sequence":"first","affiliation":[]},{"given":"R.","family":"Weiner","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02251239_CR1","unstructured":"Bader, G., Deuflhard, P.: A semi-implicit mid-point rule for stiff systems of ordinary differential equations. University of Heidelberg, SFB 123, Techn. Rep. Nr. 114 (1981)."},{"key":"BF02251239_CR2","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1137\/0716004","volume":"16","author":"K. Burrage","year":"1979","unstructured":"Burrage, K., Butcher, J. C.: Stability criteria for implicit Runge-Kutta methods. SIAM J. Numer. Anal.16, 46\u201357 (1979).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02251239_CR3","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1007\/BF01931672","volume":"15","author":"J. C. Butcher","year":"1975","unstructured":"Butcher, J. C.: A stability property of implicit Runge-Kutta methods. BIT15, 358\u2013361 (1975).","journal-title":"BIT"},{"key":"BF02251239_CR4","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF01397651","volume":"32","author":"M. Crouzeix","year":"1979","unstructured":"Crouzeix, M.: Sur Ia B-stabilit\u00e9 des m\u00e9thodes de Runge-Kutta. Numer. Math.32, 75\u201382 (1979).","journal-title":"Numer. Math."},{"key":"BF02251239_CR5","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1007\/BFb0080115","volume":"506","author":"G. Dahlquist","year":"1976","unstructured":"Dahlquist, G.: Error analysis for a class of methods for stiff non-linear initial value problems. Lecture Notes in Math.506, 60\u201374 (1976).","journal-title":"Lecture Notes in Math."},{"key":"BF02251239_CR6","series-title":"Report TRITA-NA-7906","volume-title":"Generalized disks of contractivity for explicit and implicit Runge-Kutta methods","author":"G. Dahlquist","year":"1979","unstructured":"Dahlquist, G., Jeltsch, R.: Generalized disks of contractivity for explicit and implicit Runge-Kutta methods. Report TRITA-NA-7906, Royal Institute of Technology, Stockholm, 1979."},{"key":"BF02251239_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-322-91202-2","volume-title":"Numerik gew\u00f6hnlicher Differentialgleichungen, Band 2: Mehrschrittverfahren","author":"R. D. Grigorieff","year":"1977","unstructured":"Grigorieff, R. D.: Numerik gew\u00f6hnlicher Differentialgleichungen, Band 2: Mehrschrittverfahren. Stuttgart: Teubner. 1977."},{"key":"BF02251239_CR8","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF01944478","volume":"22","author":"E. Hairer","year":"1982","unstructured":"Hairer, E., Bader, G., Lubich, Ch.: On the stability of semi-implicit methods for ordinary differential equations. BIT22, 211\u2013232 (1982).","journal-title":"BIT"},{"key":"BF02251239_CR9","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1007\/BF01933200","volume":"20","author":"E. Hairer","year":"1980","unstructured":"Hairer, E.: Highest possible order of algebraiccally stable and diagonally implicit Runge-Kutta methods. BIT20, 254\u2013256 (1980).","journal-title":"BIT"},{"key":"BF02251239_CR10","unstructured":"Hairer, E., Wanner, G.: Characterization of non-linearly stable implicit Runge-Kutta methods. Report Universit\u00e9 de Gen\u00e8ve (1980)."},{"key":"BF02251239_CR11","series-title":"Report NW 10\/74","volume-title":"Generalized linear multistep methods. I. Development of algorithms with zero-parasitic roots","author":"P. J. Houwen van der","year":"1974","unstructured":"van der Houwen, P. J., Verwer, J. G.: Generalized linear multistep methods. I. Development of algorithms with zero-parasitic roots. Report NW 10\/74, Mathematisch Centrum, Amsterdam, 1974."},{"key":"BF02251239_CR12","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF01396658","volume":"36","author":"W. H. Hundsdorfer","year":"1981","unstructured":"Hundsdorfer, W. H., Spijker, M. N.: A note on B-stability of Runge-Kutta methods. Numer. Math.36, 319\u2013333 (1981).","journal-title":"Numer. Math."},{"key":"BF02251239_CR13","series-title":"Proc. Second Manitoba Conf. on Numerical Math","volume-title":"Some numerical methods for stiff ordinary and partial differential equations","author":"J. D. Lawson","year":"1972","unstructured":"Lawson, J. D.: Some numerical methods for stiff ordinary and partial differential equations. Proc. Second Manitoba Conf. on Numerical Math (Thomas, R., Williams, H., eds.), University of Manitoba, Winnipeg, 1972."},{"key":"BF02251239_CR14","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/BF01932025","volume":"18","author":"O. Nevanlinna","year":"1978","unstructured":"Nevanlinna, O., Liniger, W.: Contractive methods for stiff differential equations. BIT18, 457\u2013474 (1978); BIT19, 53\u201372 (1979).","journal-title":"BIT"},{"key":"BF02251239_CR15","series-title":"Lecture Notes in Math.","volume-title":"An A-stable modification of the Adams-Bashforth methods","author":"S. P. N\u00f8rsett","year":"1969","unstructured":"N\u00f8rsett, S. P.: An A-stable modification of the Adams-Bashforth methods. (Lecture Notes in Math., Vol. 109.) Berlin-Heidelberg-New York: Springer 1969."},{"key":"BF02251239_CR16","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF01396634","volume":"27","author":"J. G. Verwer","year":"1977","unstructured":"Verwer, J. G.: On generalized linear multistep methods with zero-parasitic roots and an adaptive principal root. Numer. Math.27, 143\u2013155 (1977).","journal-title":"Numer. Math."},{"key":"BF02251239_CR17","series-title":"Report NW 15\/75","volume-title":"S-stability and stiff-accuracy for two classes of generalized integration methods","author":"J. G. Verwer","year":"1975","unstructured":"Verwer, J. G.: S-stability and stiff-accuracy for two classes of generalized integration methods. Report NW 15\/75, Mathematisch Centrum, Amsterdam, 1975."},{"key":"BF02251239_CR18","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/BF01941471","volume":"21","author":"J. G. Verwer","year":"1981","unstructured":"Verwer, J. G.: On the practical value of the notation of BN-stability. BIT21, 355\u2013361 (1981).","journal-title":"BIT"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02251239.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02251239\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02251239","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T13:48:40Z","timestamp":1557928120000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02251239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,12]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1983,12]]}},"alternative-id":["BF02251239"],"URL":"https:\/\/doi.org\/10.1007\/bf02251239","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,12]]}}}