{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:11:02Z","timestamp":1759191062018},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,4,19]],"date-time":"2016-04-19T00:00:00Z","timestamp":1461024000000},"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":["Math.Comput.Sci."],"published-print":{"date-parts":[[2016,9]]},"DOI":"10.1007\/s11786-016-0269-x","type":"journal-article","created":{"date-parts":[[2016,4,19]],"date-time":"2016-04-19T06:44:52Z","timestamp":1461048292000},"page":"313-329","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Towards a Lanczos\u2019 $$\\tau $$ \u03c4 -Method Toolkit for Differential Problems"],"prefix":"10.1007","volume":"10","author":[{"given":"M.","family":"Trindade","sequence":"first","affiliation":[]},{"given":"J.","family":"Matos","sequence":"additional","affiliation":[]},{"given":"P. B.","family":"Vasconcelos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,4,19]]},"reference":[{"key":"269_CR1","unstructured":"Crisci, M.R., Russo, E.: An extension of Ortiz recursive formulation of the Tau method to certain linear systems of ordinary differential equations. Math. Comput. 41(163), 27\u201342 (1983)"},{"issue":"1","key":"269_CR2","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1002\/sapm1938171123","volume":"17","author":"C Lanczos","year":"1938","unstructured":"Lanczos, C.: Trigonometric interpolation of empirical and analytical functions. J. Math. Phys. 17(1), 123\u2013199 (1938)","journal-title":"J. Math. Phys."},{"issue":"9","key":"269_CR3","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/S0898-1221(99)00275-8","volume":"38","author":"K Liu","year":"1999","unstructured":"Liu, K., Pan, C.: The automatic solution to systems of ordinary differential equations by the Tau method. Comput. Math. Appl. 38(9), 197\u2013210 (1999)","journal-title":"Comput. Math. Appl."},{"key":"269_CR4","doi-asserted-by":"crossref","DOI":"10.1201\/9781420036114","volume-title":"Chebyshev Polynomials","author":"JC Mason","year":"2002","unstructured":"Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. CRC Press, Boca Raton, Florida (2002)"},{"key":"269_CR5","unstructured":"Matos, J., Rodrigues, M.J., de\u00a0Matos, J.C.: Avoiding similarity transformations in the operational Tau method (submitted)"},{"key":"269_CR6","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.cam.2003.09.054","volume":"164","author":"J Matos","year":"2004","unstructured":"Matos, J., Rodrigues, M.J., Vasconcelos, P.B.: New implementation of the Tau method for PDEs. J. Comput. Math. Appl. 164, 555\u2013567 (2004)","journal-title":"J. Comput. Math. Appl."},{"issue":"1","key":"269_CR7","first-page":"97","volume":"40","author":"S Namasivayam","year":"1981","unstructured":"Namasivayam, S., Ortiz, E.L.: Best approximation and the numerical solution of partial differential equations with the Tau method. Port. Math. 40(1), 97\u2013119 (1981)","journal-title":"Port. Math."},{"issue":"3","key":"269_CR8","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1137\/120865458","volume":"55","author":"S Olver","year":"2013","unstructured":"Olver, S., Townsend, A.: A fast and well-conditioned spectral method. SIAM Rev. 55(3), 462\u2013489 (2013)","journal-title":"SIAM Rev."},{"key":"269_CR9","doi-asserted-by":"crossref","unstructured":"Ortiz, E.: On the numerical solution of nonlinear and functional differential equations with the Tau method. In: Numerical Treatment of Differential Equations in Applications: Proceedings, Oberwolfach, Germany, December 1977. Lecture Notes in Mathematics, vol. 679, pp. 127\u2013139. Springer, Berlin, Heidelberg (1978)","DOI":"10.1007\/BFb0067873"},{"issue":"2","key":"269_CR10","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1137\/0518035","volume":"18","author":"E Ortiz","year":"1987","unstructured":"Ortiz, E., Dinh, A.P.N.: Linear recursive schemes associated with some nonlinear partial differential equations in one dimension and the Tau method. SIAM J. Math. Anal. 18(2), 452\u2013464 (1987)","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"269_CR11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF02243435","volume":"27","author":"EL Ortiz","year":"1981","unstructured":"Ortiz, E.L., Samara, H.: An operational approach to the Tau method for the numerical solution of non-linear differential equations. Computing 27(1), 15\u201325 (1981)","journal-title":"Computing"},{"issue":"1","key":"269_CR12","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.amc.2004.09.026","volume":"168","author":"J Pour-Mahmoud","year":"2005","unstructured":"Pour-Mahmoud, J., Rahimi-Ardabili, M., Shahmorad, S.: Numerical solution of the system of fredholm integro-differential equations by the Tau method. Appl. Math. Comput. 168(1), 465\u2013478 (2005)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"269_CR13","first-page":"11","volume":"35","author":"ES Quintana-Ort\u00ed","year":"2008","unstructured":"Quintana-Ort\u00ed, E.S., Van De Geijn, R.A.: Updating an lu factorization with pivoting. ACM Trans. Math. Softw. (TOMS) 35(2), 11 (2008)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"269_CR14","doi-asserted-by":"crossref","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM (2003)","DOI":"10.1137\/1.9780898718003"},{"key":"269_CR15","doi-asserted-by":"crossref","unstructured":"Trefethen, L.N.: Spectral Methods in MATLAB, vol. 10. SIAM (2000)","DOI":"10.1137\/1.9780898719598"},{"key":"269_CR16","unstructured":"Trefethen, L.N.: Approximation Theory and Approximation Practice. SIAM (2013)"},{"key":"269_CR17","doi-asserted-by":"crossref","unstructured":"Van der Vorst, H.A.: Iterative Krylov methods for large linear systems, vol. 13. Cambridge University Press (2003)","DOI":"10.1017\/CBO9780511615115"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-016-0269-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-016-0269-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-016-0269-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-016-0269-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T22:35:11Z","timestamp":1559428511000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-016-0269-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,19]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["269"],"URL":"https:\/\/doi.org\/10.1007\/s11786-016-0269-x","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,19]]}}}