{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:26:52Z","timestamp":1762003612134,"version":"3.41.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2003,3,1]],"date-time":"2003-03-01T00:00:00Z","timestamp":1046476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,3,1]],"date-time":"2003-03-01T00:00:00Z","timestamp":1046476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Global Optimization"],"published-print":{"date-parts":[[2003,3]]},"DOI":"10.1023\/a:1022463810376","type":"journal-article","created":{"date-parts":[[2003,3,28]],"date-time":"2003-03-28T22:56:51Z","timestamp":1048892211000},"page":"283-303","source":"Crossref","is-referenced-by-count":27,"title":["Ultraspherical Integral Method for Optimal Control Problems Governed by Ordinary Differential Equations"],"prefix":"10.1007","volume":"25","author":[{"given":"H.M.","family":"El-Hawary","sequence":"first","affiliation":[]},{"given":"M.S.","family":"Salim","sequence":"additional","affiliation":[]},{"given":"H.S.","family":"Hussien","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"407291_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-84108-8","volume-title":"Spectral Methods in Fluid Dynamic","author":"C. Canuto","year":"1988","unstructured":"Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A. (1988), Spectral Methods in Fluid Dynamic, Springer, New York."},{"key":"407291_CR2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/S0377-0427(97)00228-8","volume":"89","author":"E. H. Doha","year":"1998","unstructured":"Doha, E. H. (1998), The ultraspherical coefficients of moments of a general order derivatives of an infinitely differentiable function J. Comput. and Appl. Math. 89: 53-72.","journal-title":"J. Comput. and Appl. Math."},{"key":"407291_CR3","first-page":"1","volume":"8","author":"M. Egerstedt","year":"1998","unstructured":"Egerstedt, M. and Martin, C. (1998), A control theoretic model of muscular actions in human head-eye coordination, J. of Mathematical System, Estimation and Control 8: 1-19.","journal-title":"J. of Mathematical System, Estimation and Control"},{"key":"407291_CR4","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1093\/comjnl\/12.3.282","volume":"12","author":"S.E. EL-Gendi","year":"1969","unstructured":"EL-Gendi, S.E. (1969), Chebyshev solutions of differential, integral, and integro-differential equations, Computer J. 12: 282-287.","journal-title":"Computer J."},{"issue":"6","key":"407291_CR5","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0898-1221(95)00005-J","volume":"29","author":"T. M. El-Gindy","year":"1995","unstructured":"El-Gindy, T. M., El-Hawary, H. M., Salim, M. S. and El-Kady, M. (1995), A Chebyshev approximation for solving optimal control problems, Computers Math. Appl. 29(6): 35\u201345.","journal-title":"Computers Math. Appl."},{"key":"407291_CR6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1080\/00207160008804976","volume":"75","author":"H.M. El-Hawary","year":"2000","unstructured":"El-Hawary, H.M., Salim, M.S and Hussien, H.S. (2000), Legendre spectral method for solving integral and integro-differential equations Int. J. of Computer Math. 75: 187-203.","journal-title":"Int. J. of Computer Math."},{"key":"407291_CR7","doi-asserted-by":"crossref","unstructured":"El-Hawary, H. M., Salim, M. S and Hussien, H. S. (2000), An optimal ultraspherical approximation of integrals, Int. J. of Computer Math. 77(1\/2): (to appear).","DOI":"10.1080\/00207160008805021"},{"key":"407291_CR8","unstructured":"El-Hawary, H. M. (1990), Numerical treatment of differential equations by spectral methods, Ph. D. Dissertation, Assiut University."},{"key":"407291_CR9","unstructured":"El-Kady, M. M. (1994), Numerical studies for optimal control problems, Ph.D. Thesis, Assuit University."},{"key":"407291_CR10","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0377-0427(96)00134-3","volume":"97","author":"G. M. Elnagar","year":"1997","unstructured":"Elnagar, G. M. (1997), State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems, J. Comput. and Applied Math. 97: 19-40.","journal-title":"J. Comput. and Applied Math."},{"key":"407291_CR11","volume-title":"Some successive approximation methods in control and oscillation theory","author":"P.L. Falb","year":"1969","unstructured":"Falb, P.L. and de Jong, J. L. (1969), Some successive approximation methods in control and oscillation theory, Academic Press, New York."},{"key":"407291_CR12","volume-title":"CBMS-NSF Regional Conference Series in Applied Mathematics","author":"D. Gottlieb","year":"1977","unstructured":"Gottlieb, D. and Orszag, S.A. (1977), Numerical analysis of spectral methods: theory and application, CBMS-NSF Regional Conference Series in Applied Mathematics, 26: SIAM, Philadelphia."},{"key":"407291_CR13","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/0005-1098(72)90029-5","volume":"8","author":"Y. Hontoir","year":"1972","unstructured":"Hontoir, Y. and Cruz, J. B. (1972), A manifold imbedding algorithm for optimization problems, Automatica 8: 581-588.","journal-title":"Automatica"},{"key":"407291_CR14","doi-asserted-by":"crossref","unstructured":"Jacobson, D. H. and Lele, M. M. (1969), Iee Trans. Automat. Control A C-14.","DOI":"10.1109\/TAC.1969.1099283"},{"key":"407291_CR15","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1023\/A:1008256009222","volume":"13","author":"K. Kogan","year":"1998","unstructured":"Kogan, K. and Eugene, K. (1998), Tracking demands in optimal control of managerial systems with continuously-divisible, double constrained resources, J. Global Optimization, 13: 43-59.","journal-title":"J. Global Optimization"},{"key":"407291_CR16","first-page":"103","volume":"114","author":"G. Martin","year":"2000","unstructured":"Martin, G. (2000), A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems, Journal of Comput. and Applied Math. 114: 103-119.","journal-title":"Journal of Comput. and Applied Math."},{"key":"407291_CR17","first-page":"91","volume-title":"Computing Methods in Optimization Problems","author":"H. G. Moyer","year":"1964","unstructured":"Moyer, H. G. and Pinkham, G. (1964), Several trajectory optimization techniques: Part II: Application. In: Balakrishnan, A. V. and Neustadt, L. W., (eds). Computing Methods in Optimization Problems, Academic Press, New York 91-109."},{"issue":"2","key":"407291_CR18","first-page":"1","volume":"8","author":"F. Rampazzo","year":"1998","unstructured":"Rampazzo, F. and Sartori, C. (1998), The minimum time function with unbounded control, Egerstedt and Martin, J. of Mathematical System, Estimation and Control, 8(2): 1\u201334.","journal-title":"J. of Mathematical System, Estimation and Control"},{"key":"407291_CR19","volume-title":"Numerical studied of optimal control problems and its applications","author":"M. S. Salim","year":"1990","unstructured":"Salim, M. S. (1990), Numerical studied of optimal control problems and its applications, Ph.D. Thesis, Assiut university, Egypt."},{"issue":"10","key":"407291_CR20","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1016\/0898-1221(89)90020-5","volume":"17","author":"J.A. Snyman","year":"1989","unstructured":"Snyman, J.A. (1989), A convergent dynamic method for large minimization problems, Computers Math. Appl. 17(10): 1369-1377.","journal-title":"Computers Math. Appl."},{"key":"407291_CR21","unstructured":"Szeg\u00f6, (1985), Orthogonal Polynomials, Am. Math. Soc. Colloq. Pub. 23."},{"key":"407291_CR22","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1109\/TAC.1972.1099886","volume":"17","author":"J.M. Taylor","year":"1972","unstructured":"Taylor, J.M. and Constantinides, C. T. (1972), Optimization: application of the epsilon method, IEEE Trans. Automat. Contr. Ac. 17: 128-131.","journal-title":"IEEE Trans. Automat. Contr. Ac."},{"issue":"4","key":"407291_CR23","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1109\/9.192187","volume":"33","author":"R. Van Dooren","year":"1988","unstructured":"Van Dooren, R. and Vlassenbroeck, J. (1988), A Chebyshev technique for solving nonlinear optimal control problems, IEEE Trans. Automat. Contr., 33(4): 333-339.","journal-title":"IEEE Trans. Automat. Contr."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1022463810376.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1022463810376\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1022463810376.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:45:24Z","timestamp":1751366724000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1022463810376"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["407291"],"URL":"https:\/\/doi.org\/10.1023\/a:1022463810376","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}