{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1504"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1504","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"Αριθμητική επίλυση συνήθων διαφορικών εξισώσεων με περιοδική λύση","abstract":"The subject of this dissertation is the study of the numerical solution of the second order initial-value problem, the solution of which presents a periodical behaviour. Numerical methods for the numerical solution of the above general problem are being expounded. At first, a sixth order exponentially fitting method, which requires the a priori knowledge of the frequency of the problem, is being expounded. In the same category a four-step exponentially fitting method is being expounded. Afterwards, explicit and implicit methods with phase-lag of order six and eight, a part of which are P-stable while the rest have a larger interval of periodicity than the corresponding classical ones, are being expounded. These methods do not require the a priori knowledge of the frequency of the problem. In the same category an eight order hybrid method with phase-lag of order eight and with a large interval of periodicity is being expounded.","abstract_html":"The subject of this dissertation is the study of the numerical solution of the second order initial-value problem, the solution of which presents a periodical behaviour. Numerical methods for the numerical solution of the above general problem are being expounded. At first, a sixth order exponentially fitting method, which requires the a priori knowledge of the frequency of the problem, is being expounded. In the same category a four-step exponentially fitting method is being expounded. Afterwards, explicit and implicit methods with phase-lag of order six and eight, a part of which are P-stable while the rest have a larger interval of periodicity than the corresponding classical ones, are being expounded. These methods do not require the a priori knowledge of the frequency of the problem. In the same category an eight order hybrid method with phase-lag of order eight and with a large interval of periodicity is being expounded.","abstract_has_math":false,"creators":["Simos, Theodore","Σίμος, Θεόδωρος"],"institution":"National Technical University of Athens (NTUA)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-24T02:24:59Z","subjects":["Άμεση μέθοδος","Αριθμητική επίλυση διαφορικών εξισώσεων","Δευτέρας τάξεως πρόβλημα αρχικών τιμών","Διαφορά φάσης","Εκθετικές μέθοδοι","Έμμεση μέθοδος","Ιδιοτιμή","Περιοδική ευστάθεια","Περιοδική λύση","Υστέρηση φάσης","Ergenvalue","Explicit methods","Exponential-fitting-methods","Implicit methods","Periodical solutions","Periodical stability","Phase-lag","Second order initial-value problem","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1504"],"render_values":[{"text":"10.12681/eadd/1504","href":"https://doi.org/10.12681/eadd/1504","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1504","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Simos, Theodore","Σίμος, Θεόδωρος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1990"]},{"key":"dc:publisher","label":"Institution","values":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Άμεση μέθοδος","Αριθμητική επίλυση διαφορικών εξισώσεων","Δευτέρας τάξεως πρόβλημα αρχικών τιμών","Διαφορά φάσης","Εκθετικές μέθοδοι","Έμμεση μέθοδος","Ιδιοτιμή","Περιοδική ευστάθεια","Περιοδική λύση","Υστέρηση φάσης","Ergenvalue","Explicit methods","Exponential-fitting-methods","Implicit methods","Periodical solutions","Periodical stability","Phase-lag","Second order initial-value problem","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1504","http://hdl.handle.net/10442/hedi/1504"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The subject of this dissertation is the study of the numerical solution of the second order initial-value problem, the solution of which presents a periodical behaviour. Numerical methods for the numerical solution of the above general problem are being expounded. At first, a sixth order exponentially fitting method, which requires the a priori knowledge of the frequency of the problem, is being expounded. In the same category a four-step exponentially fitting method is being expounded. Afterwards, explicit and implicit methods with phase-lag of order six and eight, a part of which are P-stable while the rest have a larger interval of periodicity than the corresponding classical ones, are being expounded. These methods do not require the a priori knowledge of the frequency of the problem. In the same category an eight order hybrid method with phase-lag of order eight and with a large interval of periodicity is being expounded.","Στην παρούσα διατριβή μελετάται η αριθμητική επίλυση του προβλήματος αρχικών τιμών δευτέρας τάξεως, του οποίου η λύση παρουσιάζει περιοδική συμπεριφορά. Αναπτύσσονται αριθμητικές μέθοδοι για την αριθμητική επίλυση του παραπάνω γενικού προβλήματος. Καταρχήν αναπτύσσεται μια έκτης τάξεως exponentially fitting μέθοδος, η οποία προαπαιτεί την γνώση της συχνότητας του προβλήματος. Στην ίδια κατηγορία αναπτύσσεται και μία τεσσάρων βημάτων exponentially fitting μέθοδος. Κατόπιν αναπτύσσονται μέθοδοι explicit και implict με phase-lag έκτης και ογδόης τάξεως εκ των οποίων άλλες είναι P-stable και άλλες έχουν μεγαλύτερο διάστημα περιοδικότητας από τις αντίστοιχες κλασσικές. Οι εν λόγω μέθοδοι δεν προαπαιτούν την γνώση της συχνότητας του προβλήματος. Στην ίδια κατηγορία αναπτύσσεται και μία υβριδική μέθοδος ογδόης τάξεως με phase-lag τάξεως ογδόης και με μεγάλο διάστημα περιοδικότητας."]},{"key":"dc:title","label":"Title","values":["Αριθμητική επίλυση συνήθων διαφορικών εξισώσεων με περιοδική λύση","Numerical solution of ordinary differential equations with personal solution"]}]}],"canonical_facts":{"dc:creator":["Simos, Theodore","Σίμος, Θεόδωρος"],"dc:date":["1990"],"dc:description":["The subject of this dissertation is the study of the numerical solution of the second order initial-value problem, the solution of which presents a periodical behaviour. Numerical methods for the numerical solution of the above general problem are being expounded. At first, a sixth order exponentially fitting method, which requires the a priori knowledge of the frequency of the problem, is being expounded. In the same category a four-step exponentially fitting method is being expounded. Afterwards, explicit and implicit methods with phase-lag of order six and eight, a part of which are P-stable while the rest have a larger interval of periodicity than the corresponding classical ones, are being expounded. These methods do not require the a priori knowledge of the frequency of the problem. In the same category an eight order hybrid method with phase-lag of order eight and with a large interval of periodicity is being expounded.","Στην παρούσα διατριβή μελετάται η αριθμητική επίλυση του προβλήματος αρχικών τιμών δευτέρας τάξεως, του οποίου η λύση παρουσιάζει περιοδική συμπεριφορά. Αναπτύσσονται αριθμητικές μέθοδοι για την αριθμητική επίλυση του παραπάνω γενικού προβλήματος. Καταρχήν αναπτύσσεται μια έκτης τάξεως exponentially fitting μέθοδος, η οποία προαπαιτεί την γνώση της συχνότητας του προβλήματος. Στην ίδια κατηγορία αναπτύσσεται και μία τεσσάρων βημάτων exponentially fitting μέθοδος. Κατόπιν αναπτύσσονται μέθοδοι explicit και implict με phase-lag έκτης και ογδόης τάξεως εκ των οποίων άλλες είναι P-stable και άλλες έχουν μεγαλύτερο διάστημα περιοδικότητας από τις αντίστοιχες κλασσικές. Οι εν λόγω μέθοδοι δεν προαπαιτούν την γνώση της συχνότητας του προβλήματος. Στην ίδια κατηγορία αναπτύσσεται και μία υβριδική μέθοδος ογδόης τάξεως με phase-lag τάξεως ογδόης και με μεγάλο διάστημα περιοδικότητας."],"dc:identifier":["10.12681/eadd/1504","http://hdl.handle.net/10442/hedi/1504"],"dc:language":["gre"],"dc:publisher":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"],"dc:subject":["Άμεση μέθοδος","Αριθμητική επίλυση διαφορικών εξισώσεων","Δευτέρας τάξεως πρόβλημα αρχικών τιμών","Διαφορά φάσης","Εκθετικές μέθοδοι","Έμμεση μέθοδος","Ιδιοτιμή","Περιοδική ευστάθεια","Περιοδική λύση","Υστέρηση φάσης","Ergenvalue","Explicit methods","Exponential-fitting-methods","Implicit methods","Periodical solutions","Periodical stability","Phase-lag","Second order initial-value problem","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["Αριθμητική επίλυση συνήθων διαφορικών εξισώσεων με περιοδική λύση","Numerical solution of ordinary differential equations with personal solution"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:59Z"}