{ "article_id": 856, "public_id": "7d397806-f1bd-4335-87ee-c67fd1be3067", "internal_identifier": null, "source_identifier": "39:221", "status": "published", "type": "research_article", "title": "SOLVING A CLASS OF TRANSMISSION PROBLEMS BY THE DIFFERENTIAL TRANSFORM METHOD", "title_secondary": null, "abstract": "There are various numerical methods for solving many problems in\r\nmathematical physics. The differential transform method (DTM) is one of the\r\nnumerical methods for solving ordinary and partial differential equations. The\r\nconcept of the differential transform was first proposed by Zhou. Zhou’s aim was\r\nto solve both linear and non-linear initial value problems in electric circuit analysis. In this work, we study the performance of the DTM applied to the solution\r\nof boundary value problems for Sturm-Liouville equation with additional transmission conditions at one interior singular point. Note that, the present method\r\ncan be applied to many initial value problems and boundary-value problems with\r\nadditional transmission conditions and does not require linearization, perturbation\r\nor discretization.  ", "language": "en", "english_title": null, "english_abstract": null, "doi": null, "doi_url": null, "resource_url": "https://www.set-science.com/a/7d397806-f1bd-4335-87ee-c67fd1be3067", "pdf_url": "https://www.set-science.com/a/7d397806-f1bd-4335-87ee-c67fd1be3067/pdf", "og_image": "https://www.set-science.com/assets/img/og-card-v2.png", "authors": [ { "public_id": "1fd61767-6add-4f25-8755-2b9968b29fe9", "given": "Merve", "family": "Yücel", "full": "Merve Yücel", "literal": null, "orcid": null, "orcid_url": null, "email": "merve.yucel@outlook.com", "corresponding": false, "sequence": "first", "affiliations": [ { "name": "Hitit University", "department": null, "country": null, "country_code": null, "ror": null, "ror_url": null } ] }, { "public_id": "4be51fa3-90c0-469c-ad1c-c3584dc28db2", "given": "Kadriye", "family": "Aydemir", "full": "Kadriye Aydemir", "literal": null, "orcid": null, "orcid_url": null, "email": "kadriyeaydemir@gmail.com", "corresponding": false, "sequence": "additional", "affiliations": [ { "name": "Amasya University", "department": null, "country": null, "country_code": null, "ror": null, "ror_url": null } ] }, { "public_id": "c2602dac-fef2-409f-864c-a002c93f9a87", "given": "O. Sh. ", "family": "MUKHTAROV ", "full": "O. Sh.  MUKHTAROV ", "literal": null, "orcid": null, "orcid_url": null, "email": "omuktarov@yahoo.com", "corresponding": true, "sequence": "additional", "affiliations": [ { "name": "Azerbaijan National Academy of Sciences  ", "department": null, "country": null, "country_code": null, "ror": null, "ror_url": null } ] } ], "keywords": [ "Differential transform method, transmission conditions, approximation solution" ], "translations": [ { "language": "en", "title": "SOLVING A CLASS OF TRANSMISSION PROBLEMS BY THE DIFFERENTIAL TRANSFORM METHOD", "abstract": "There are various numerical methods for solving many problems in\r\nmathematical physics. The differential transform method (DTM) is one of the\r\nnumerical methods for solving ordinary and partial differential equations. The\r\nconcept of the differential transform was first proposed by Zhou. Zhou’s aim was\r\nto solve both linear and non-linear initial value problems in electric circuit analysis. In this work, we study the performance of the DTM applied to the solution\r\nof boundary value problems for Sturm-Liouville equation with additional transmission conditions at one interior singular point. Note that, the present method\r\ncan be applied to many initial value problems and boundary-value problems with\r\nadditional transmission conditions and does not require linearization, perturbation\r\nor discretization.  \r\n", "keywords": [ "Differential transform method, transmission conditions, approximation solution" ] } ], "subjects": [], "subject_names": [], "published_date": "2018-12-31", "published_year": "2018", "received_date": null, "accepted_date": null, "volume": "3", "issue": null, "page_first": "1158", "page_last": "1162", "article_number": null, "conference": { "short_name": "ISAS2018-Winter", "full_title": "2nd International Symposium on Innovative Approaches in Scientific Studies", "name": "2nd International Symposium on Innovative Approaches in Scientific Studies", "acronym": "ISAS2018-Winter", "location": "Samsun, Türkiye", "start_date": "2018-11-30", "end_date": null, "public_id": "b8a703cc-09f7-4d5b-ae60-eb31a1050720" }, "proceedings": { "title": "2nd International Symposium on Innovative Approaches in Scientific Studies", "series_title": "Setsci conference indexing system", "publisher": "SET Technology", "isbn": null, "eisbn": null, "issn": "2618-6446", "eissn": null, "doi": null, "doi_prefix": null, "slug": "setsci-volume-3-2018-legacy-39", "public_id": "641f522e-9cf0-4c89-be17-c6037f3d1bca", "url": "https://www.set-science.com/p/setsci-volume-3-2018-legacy-39" }, "license": { "name": "CC BY 4.0", "url": "https://creativecommons.org/licenses/by/4.0/", "code": "CC-BY-4.0", "open_access": true }, "copyright": { "holder": "SET Technology", "year": "2018" }, "funding_statement": null, "funders": [], "references": [ { "order": 1, "raw": "J. K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986 (in Chinese).", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 2, "raw": "A. Saravanan and N. Magesh A Comparison between the reduced differential transform method and the Adomian decomposition method for the NewellWhitehead-Segel equation, Journal of the Egyptian Mathematical Society, 21(2013), 259-265.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 3, "raw": "A. H. Ali and S. A. Mustafa, Applications of differential transform method to integral equations , American Journal of Engineering Research, Volume.7(2018), Issue.1, 271-276.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 4, "raw": "V. S. Ertrk, Differential transformation method for solving differential equations of Lane-Emden Type, Mathematical and Computational Applications, Vol.12(2007), No.3, 135-139.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 5, "raw": "A.S.V.R. Kanth and K. Aruna Solution of singular two-point boundary value problems using differential transformation method, Physics Letters A, 372(2008), 4671-4673.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 6, "raw": "H. Fatoorehchi and H. Abolghasemi, Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials, Applied Mathematical Modelling, 37(2013), 6008-6017.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 7, "raw": "I.H. Abdel-Halim Hassan, Different applications for the differential transformation in the differential equations, Applied Mathematics and Computation, 129(2002), 183201.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 8, "raw": "I. H. Abdel-Halim Hassan and V. S. Ertrk, Applying Differential Transformation Method to the One-Dimensional Planar Bratu Problem, Int. J. Contemp. Math. Sciences, Vol.2(2007), no.30, 1493 - 1504.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null } ], "statements": { "acknowledgements": null, "conflict_of_interest": null, "data_availability": null, "ai_disclosure": null }, "credit": [], "history": { "published": "2018-12-31" } }