{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:33:25Z","timestamp":1774953205439,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,11,29]],"date-time":"2017-11-29T00:00:00Z","timestamp":1511913600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571238"],"award-info":[{"award-number":["11571238"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s10915-017-0616-3","type":"journal-article","created":{"date-parts":[[2017,11,29]],"date-time":"2017-11-29T17:49:05Z","timestamp":1511977745000},"page":"166-188","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["A Spectral Collocation Method for Nonlinear Fractional Boundary Value Problems with a Caputo Derivative"],"prefix":"10.1007","volume":"76","author":[{"given":"Chuanli","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongqing","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lilian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,11,29]]},"reference":[{"key":"616_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-30726-6","volume-title":"Spectral Methods: Fundamentals in Single Domains","author":"C Canuto","year":"2006","unstructured":"Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods: Fundamentals in Single Domains. Springer, Berlin (2006)"},{"key":"616_CR2","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1090\/mcom3035","volume":"85","author":"S Chen","year":"2016","unstructured":"Chen, S., Shen, J., Wang, L.L.: Generalized Jacobi functions and their applications to fractional differential equations. Math. Comput. 85, 1603\u20131638 (2016)","journal-title":"Math. Comput."},{"key":"616_CR3","doi-asserted-by":"crossref","first-page":"018302","DOI":"10.1103\/PhysRevLett.91.018302","volume":"91","author":"D del-Castillo-Negrete","year":"2003","unstructured":"del-Castillo-Negrete, D., Carreras, B.A., Lynch, V.E.: Front dynamics in reaction\u2013diffusion systems with Levy fights: a fractional diffusion approach. Phys. Rev. Lett. 91, 018302 (2003)","journal-title":"Phys. Rev. Lett."},{"key":"616_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lecture Notes in Mathematics","author":"K Diethelm","year":"2010","unstructured":"Diethelm, K.: The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lecture Notes in Mathematics, vol. 2004. Springer, Berlin (2010)"},{"key":"616_CR5","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1002\/num.20112","volume":"22","author":"VJ Ervin","year":"2006","unstructured":"Ervin, V.J., Roop, J.P.: Variational formulation for the stationary fractional advection dispersion equation. Numer. Methods Partial Differ. Equ. 22, 558\u2013576 (2006)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"616_CR6","doi-asserted-by":"crossref","first-page":"3646","DOI":"10.1016\/j.cnsns.2010.12.008","volume":"16","author":"S Esmaeili","year":"2011","unstructured":"Esmaeili, S., Shamsi, M.: A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 16, 3646\u20133654 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"616_CR7","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1515\/fca-2016-0019","volume":"19","author":"K Ito","year":"2016","unstructured":"Ito, K., Jin, B., Takeuchi, T.: On a Legendre tau method for fractional boundary value problems with a Caputo derivative. Fract. Calc. Appl. Anal. 19, 357\u2013378 (2016)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"616_CR8","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1090\/mcom\/2960","volume":"84","author":"B Jin","year":"2015","unstructured":"Jin, B., Lazarov, R., Pasciak, J., Rundell, W.: Variational formulation of problems involving fractional order differential operators. Math. Comput. 84, 2665\u20132700 (2015)","journal-title":"Math. Comput."},{"key":"616_CR9","doi-asserted-by":"crossref","first-page":"2272","DOI":"10.1137\/13093933X","volume":"52","author":"B Jin","year":"2014","unstructured":"Jin, B., Lazarov, R., Pasciak, J., Zhou, Z.: Error analysis of a finite element method for the space-fractional parabolic equation. SIAM J. Numer. Anal. 52, 2272\u20132294 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"616_CR10","volume-title":"Theory and Applications of Fractional Differential Equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)"},{"key":"616_CR11","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1007\/s10543-014-0539-4","volume":"55","author":"N Kopteva","year":"2015","unstructured":"Kopteva, N., Stynes, M.: An efficient collocation method for a Caputo two-point boundary value problem. BIT 55, 1105\u20131123 (2015)","journal-title":"BIT"},{"key":"616_CR12","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2478\/s13540-012-0028-x","volume":"15","author":"C Li","year":"2012","unstructured":"Li, C., Zeng, F., Liu, F.: Spectral approximations to the fractional integral and derivative. Fract. Calc. Appl. Anal. 15, 383\u2013406 (2012)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"616_CR13","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1137\/080718942","volume":"47","author":"X Li","year":"2009","unstructured":"Li, X., Xu, C.: A space-time spectral method for the time fractional diffusion equation. SIAM J. Numer. Anal. 47, 2108\u20132131 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"616_CR14","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.cnsns.2010.05.027","volume":"16","author":"JT Machado","year":"2011","unstructured":"Machado, J.T., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16, 1140\u20131153 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"616_CR15","doi-asserted-by":"crossref","DOI":"10.1142\/p614","volume-title":"Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models","author":"F Mainardi","year":"2010","unstructured":"Mainardi, F.: Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Press, London (2010)"},{"key":"616_CR16","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/S0377-0427(00)00557-4","volume":"134","author":"G Mastroianni","year":"2001","unstructured":"Mastroianni, G., Occorsto, D.: Optimal systems of nodes for Lagrange interpolation on bounded intervals: a survey. J. Comput. Appl. Math. 134, 325\u2013341 (2001)","journal-title":"J. Comput. Appl. Math."},{"key":"616_CR17","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s11075-011-9465-6","volume":"58","author":"P Mokhtary","year":"2011","unstructured":"Mokhtary, P., Ghoreishi, F.: The $$L^2$$ L 2 -convergence of the Legendre spectral tau matrix formulation for nonlinear fractional integro-differential equations. Numer. Algor. 58, 475\u2013496 (2011)","journal-title":"Numer. Algor."},{"key":"616_CR18","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1016\/j.cam.2012.03.002","volume":"236","author":"A Pedas","year":"2012","unstructured":"Pedas, A., Tamme, E.: Piecewise polynomial collocation for linear boundary value problems of fractional differential equations. J. Comput. Appl. Math. 236, 3349\u20133359 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"616_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71041-7","volume-title":"Spectral Methods: Algorithms, Analysis and Applications, Springer Series in Computational Mathematics","author":"J Shen","year":"2011","unstructured":"Shen, J., Tang, T., Wang, L.L.: Spectral Methods: Algorithms, Analysis and Applications, Springer Series in Computational Mathematics, vol. 41. Springer, Berlin (2011)"},{"key":"616_CR20","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.jcp.2005.08.008","volume":"213","author":"C Tadjeran","year":"2006","unstructured":"Tadjeran, C., Meerschaert, M.M., Scheffler, H.P.: A second-order accurate numerical approximation for the fractional diffusion equation. J. Comput. Phys. 213, 205\u2013213 (2006)","journal-title":"J. Comput. Phys."},{"key":"616_CR21","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1137\/130932776","volume":"52","author":"H Wang","year":"2014","unstructured":"Wang, H., Yang, D., Zhu, S.: Inhomogeneous dirichlet boundary-value problems of space-fractional diffusion equations and their finite element approximations. SIAM J. Numer. Anal. 52, 1292\u20131310 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"616_CR22","doi-asserted-by":"crossref","first-page":"2285","DOI":"10.1090\/mcom\/3183","volume":"86","author":"ZQ Wang","year":"2017","unstructured":"Wang, Z.Q., Guo, Y.L., Yi, L.J.: An $$hp$$ hp -version Legendre\u2013Jacobi spectral collocation method for Volterra integro-differential equations with smooth and weakly singular kernels. Math. Comput. 86, 2285\u20132324 (2017)","journal-title":"Math. Comput."},{"key":"616_CR23","first-page":"635","volume":"85","author":"ZQ Wang","year":"2016","unstructured":"Wang, Z.Q., Sheng, C.T.: An $$hp$$ hp -spectral collocation method for nonlinear Volterra integral equations with vanishing variable delays. Math. Comput. 85, 635\u2013666 (2016)","journal-title":"Math. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0616-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0616-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0616-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T14:22:01Z","timestamp":1693318921000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0616-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,29]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["616"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0616-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,29]]}}}