{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:41:24Z","timestamp":1777902084545,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"11","license":[{"start":{"date-parts":[[2004,11,1]],"date-time":"2004-11-01T00:00:00Z","timestamp":1099267200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2004,11]]},"abstract":"<jats:p>Although boundary control of linear partial differential equations has become an important research area, there is still no readily available simulation tool to help researchers analyze and design. In this article, a simulation method for some typical boundary control problems, combining symbolic math and a numerical method, is presented with application examples. In the intermediate steps of the simulation, an important by-product, transfer function of the controlled system, can be obtained, which makes the design of more advanced boundary controllers possible and much easier.<\/jats:p>","DOI":"10.1177\/0037549704050183","type":"journal-article","created":{"date-parts":[[2005,4,11]],"date-time":"2005-04-11T13:04:06Z","timestamp":1113224646000},"page":"635-643","source":"Crossref","is-referenced-by-count":12,"title":["A Hybrid Symbolic-Numerical Simulation Method for Some Typical Boundary                 Control Problems"],"prefix":"10.1177","volume":"80","author":[{"given":"Jinsong","family":"Liang","sequence":"first","affiliation":[{"name":"Center for Self-Organizing and Intelligent Systems (CSOIS), Department of                         Electrical and Computer Engineering, 4160 Old Main Hill, Utah State                         University, Logan, UT 84322-4160"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YangQuan","family":"Chen","sequence":"additional","affiliation":[{"name":"Center for Self-Organizing and Intelligent Systems (CSOIS), Department of                         Electrical and Computer Engineering, 4160 Old Main Hill, Utah State                         University, Logan, UT 84322-4160,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bao-Zhu","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Systems Sciences, Academy of Mathematics and System                         Sciences, Academia Sinica, Beijing 100080, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2004,11,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00252-7"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/9.975475"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996302366"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/9.654893"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012999354880"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900372519"},{"key":"atypb7","volume-title":"Partial differential equation (PDE) tool box user\u2019s guide","year":"2002"},{"key":"atypb8","volume-title":"The finite difference method in partial differential equations","author":"Mitchell, A. R.","year":"1980"},{"key":"atypb9","volume-title":"Advanced engineering mathematics","author":"Jeffrey, A.","year":"2002"},{"key":"atypb10","volume-title":"Symbolic math toolbox user\u2019s guide","year":"2002"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1145\/155743.155788"},{"key":"atypb12","first-page":"27","volume-title":"Konference MATLAB \u201999 ZCU Plzen","author":"Bran\u010d\u00edk, L."},{"key":"atypb13","first-page":"809","volume-title":"Proceedings of the 41st IEEE Conference on Decision and Control","author":"Liang, J."},{"key":"atypb14","first-page":"97","volume-title":"Proceedings of the 5th EDS 98 International Conference","author":"Bran\u010d\u00edk, L."},{"key":"atypb15","unstructured":"Bran\u010d\u00edk, L. 1999. An improvement of FFT-based numerical                 ILT procedure by application of \u03b5-algorithm. In\n                      Sborn\u00edk                     p\u0159edn\u00e1\u0161ek modern\u00ed sm\u011bry                     v\u00fduky elektrotechniky a elektroniky STO-7\n                      , Brno,                 Z\u00e1\u0159\u00ed, pp. 196-9."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/pssb.2221330150"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1063\/1.527251"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1063\/1.528578"},{"key":"atypb19","volume-title":"Proceedings of the 36th IEEE Conference on Decision and Control","author":"Mainardi, F."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016539022492"},{"key":"atypb21","volume-title":"The First IFAC Symposium on Fractional Derivatives and Applications (FDA\u201904)","author":"Liang, J."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1967.tb02303.x"},{"key":"atypb23","volume-title":"Fractional differential equations","author":"Podlubny, I.","year":"1999"},{"key":"atypb24","volume-title":"Structural analysis (Pws-Kent series in Engineering)","author":"Kassimali, A.","year":"1993"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/0325029"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/0324007"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1109\/9.186332"},{"key":"atypb28","volume-title":"The control handbook","author":"Levine, W.","year":"1996"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549704050183","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549704050183","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:18:51Z","timestamp":1777634331000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549704050183"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11]]},"references-count":28,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2004,11]]}},"alternative-id":["10.1177\/0037549704050183"],"URL":"https:\/\/doi.org\/10.1177\/0037549704050183","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,11]]}}}