{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:05:27Z","timestamp":1762506327541},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2014,5,9]],"date-time":"2014-05-09T00:00:00Z","timestamp":1399593600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s11075-014-9870-8","type":"journal-article","created":{"date-parts":[[2014,5,8]],"date-time":"2014-05-08T03:48:30Z","timestamp":1399520910000},"page":"741-768","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Numerical solution of Volterra integro-differential equations by superimplicit multistep collocation methods"],"prefix":"10.1007","volume":"68","author":[{"given":"Somayyeh","family":"Fazeli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gholamreza","family":"Hojjati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,5,9]]},"reference":[{"key":"9870_CR1","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1137\/0716066","volume":"16","author":"CTH Baker","year":"1979","unstructured":"Baker, C.T.H., Makroglou, A., Short, E.: Regions of stability in the numerical treatment of Volterra integro-differential equations. SIAM J. Numer. Anal. 16, 890\u2013910 (1979)","journal-title":"SIAM J. Numer. Anal."},{"key":"9870_CR2","unstructured":"Brunner, H., Van der Houwen, P.J.: The Numerical solution of Volterra equations, CWI monographs, vol. 3, North Holland, Amesterdam (1986)"},{"key":"9870_CR3","doi-asserted-by":"crossref","unstructured":"Brunner, H.: Collocation methods for Volterra integral and related functional equations. Cambridge University Press (2004)","DOI":"10.1017\/CBO9780511543234"},{"issue":"1","key":"9870_CR4","first-page":"75","volume":"12","author":"H Brunner","year":"1974","unstructured":"Brunner, H., Lambert, J.D.: Stability of numerical methods for Volterra integro-differential equations. Comput. (ArchElektron. Rechnen) 12(1), 75\u201389 (1974)","journal-title":"Comput. (ArchElektron. Rechnen)"},{"key":"9870_CR5","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1016\/j.amc.2013.07.012","volume":"221","author":"A Cardone","year":"2013","unstructured":"Cardone, A., Conte, D.: Multistep collocation methods for Volterra integro-differential equations. Appl. Math. Comput. 221, 770\u2013785 (2013)","journal-title":"Appl. Math. Comput."},{"key":"9870_CR6","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/BF01396701","volume":"34","author":"JR Cash","year":"1980","unstructured":"Cash, J.R.: On the integration of stiff systems of ODEs using extended backward differentiation formula. Numer. Math. 34, 235\u2013246 (1980)","journal-title":"Numer. Math."},{"key":"9870_CR7","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1137\/0718003","volume":"18","author":"JR Cash","year":"1981","unstructured":"Cash, J.R.: Second derivative extended backward differentiation formulas for the numerical integration of stiff systems. SIAM J. Numer. Anal. 18, 21\u201336 (1981)","journal-title":"SIAM J. Numer. Anal."},{"key":"9870_CR8","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1016\/j.apnum.2009.01.001","volume":"59","author":"D Conte","year":"2009","unstructured":"Conte, D., Paternoster, B.: Multistep collocation methods for Volterra Integral equations. Appl. Numer. Math. 59, 1721\u20131736 (2009)","journal-title":"Appl. Numer. Math."},{"key":"9870_CR9","doi-asserted-by":"crossref","unstructured":"Dahlquist, G.: A special stability problem for linear multistep methods, BIT 3. 27-43 (1963)","DOI":"10.1007\/BF01963532"},{"key":"9870_CR10","doi-asserted-by":"crossref","first-page":"143","DOI":"10.3846\/13926292.2003.9637219","volume":"8","author":"A Makroglou","year":"2003","unstructured":"Makroglou, A.: Integral equations and actuarial risk management: Some models and numerics. Math. Model. Anal. 8, 143-154 (2003)","journal-title":"Math. Model. Anal."},{"key":"9870_CR11","volume-title":"Fourier Series and Integrals","author":"H Dym","year":"1972","unstructured":"Dym, H., McKean, H. P.: Fourier Series and Integrals. Academic Press, New York (1972)"},{"key":"9870_CR12","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1016\/j.mcm.2011.08.034","volume":"55","author":"S Fazeli","year":"2012","unstructured":"Fazeli, S., Hojjati, G., Shahmorad, S.: Superimplicit multistep collocation methods for nonlinear Volterra integral equations. Math. Comput. Model. 55, 590\u2013607 (2012)","journal-title":"Math. Comput. Model."},{"key":"9870_CR13","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0021-9045(73)90079-8","volume":"9","author":"Ferguson D.","year":"1973","unstructured":"Ferguson D.: Some interpolation theorems for polynomials. Journal of approximation theory 9, 327\u2013348 (1973)","journal-title":"Journal of approximation theory"},{"key":"9870_CR14","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.apm.2005.06.007","volume":"30","author":"G Hojjati","year":"2006","unstructured":"Hojjati, G., Rahimi Ardabili, M.Y., Hosseini, S.M.: New second derivative multistep methods for stiff systems. Appl. Math. Model. 30, 466\u2013476 (2006)","journal-title":"Appl. Math. Model."},{"key":"9870_CR15","volume-title":"Numerical Methods for Ordinary Differential Systems","author":"Lambert J.D.","year":"1991","unstructured":"Lambert J.D.: Numerical Methods for Ordinary Differential Systems. Wiley, New York (1991)"},{"key":"9870_CR16","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1145\/321510.321521","volume":"16","author":"P Linz","year":"1969","unstructured":"Linz, P.: Linear multistep methods for Volterra integro-differential equations. J. Ass. comput. Mach. 16, 295\u2013301 (1969)","journal-title":"J. Ass. comput. Mach."},{"key":"9870_CR17","doi-asserted-by":"crossref","unstructured":"Mehdiyeva, G., Imanova, M., Ibrahimov, V.: Application of the Hybrid methods to solving Volterra integro-differential equations, World Academy of Science. Eng. Technol. 77 (2011)","DOI":"10.1063\/1.4765535"},{"key":"9870_CR18","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF01399087","volume":"27","author":"J Matthys","year":"1976\/77","unstructured":"Matthys, J.: A-stable linear multistep methods for Volterra integro-differential equations. Numer. Math. 27, 85\u201394 (1976\/77)","journal-title":"Numer. Math."},{"key":"9870_CR19","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/0022-247X(66)90160-0","volume":"16","author":"IJ Schoenberg","year":"1966","unstructured":"Schoenberg, I.J.: On Hermite-Birkhoff interpolation. J. Math. Anal. Appl. 16, 538-543 (1966)","journal-title":"J. Math. Anal. Appl."},{"key":"9870_CR20","doi-asserted-by":"crossref","unstructured":"Stoer, J., Bulirsch, R.: Introduction to numerical analysis. Springer (2002)","DOI":"10.1007\/978-0-387-21738-3"},{"key":"9870_CR21","unstructured":"Volterra, V.: Theory of functional and of integral and integrodifferential equations, Moscow, Nauka (1982)"},{"key":"9870_CR22","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1093\/imanum\/2.2.131","volume":"2","author":"PHM Wolkenfelt","year":"1982","unstructured":"Wolkenfelt, P.H.M.: The Construction of Reducible Quadrature Rules for Volterra Integral and Integro-differential Equations. IMA J. Numer. Anal. 2, 131\u2013152 (1982)","journal-title":"IMA J. Numer. Anal."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9870-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-014-9870-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9870-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,10]],"date-time":"2019-08-10T08:32:02Z","timestamp":1565425922000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-014-9870-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,9]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["9870"],"URL":"https:\/\/doi.org\/10.1007\/s11075-014-9870-8","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,9]]}}}