{"id":{"repo_id":"greece","oai_identifier":"oai:10442/0600"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/0600","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΜΕΘΟΔΟΙ ΠΑΡΕΜΒΟΛΗΣ ΜΕ Ο(Η6) ΣΥΓΚΛΙΣΗ ΓΙΑ ΕΛΛΕΙΠΤΙΚΕΣ ΕΞΙΣΩΣΕΙΣ 2ΗΣ ΚΑΙ 4ΗΣ ΤΑΞΗΣ","abstract":"IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE APPROXIMATION SOLUTIONS AREPIECEWISE POLYNOMIALS OF DEGREE 5, IN THE SPACE C4. WE MAKE A THEORETICAL STUDYING OF THESE METHODS AND WE PROVE THEIR OPTIMAL CONVERGENCE. WE ALSO PRESENT THE COMPUTATIONAL BEHAVIOUR OF THE OPTIMAL QUINTIC SPLINE COLLOCATION METHOD.","abstract_html":"IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE APPROXIMATION SOLUTIONS AREPIECEWISE POLYNOMIALS OF DEGREE 5, IN THE SPACE C4. WE MAKE A THEORETICAL STUDYING OF THESE METHODS AND WE PROVE THEIR OPTIMAL CONVERGENCE. WE ALSO PRESENT THE COMPUTATIONAL BEHAVIOUR OF THE OPTIMAL QUINTIC SPLINE COLLOCATION METHOD.","abstract_has_math":false,"creators":["Ηροδότου-Έλληνα, Μαρίνα","Irodotou-Ellina, Marina"],"institution":"Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1987,"date_issued":"1987","date_published":"1987","updated_at":"2026-07-24T02:25:21Z","subjects":["Collocation","Differential equations","Interpolation","QUINTIC SPLINES","Διαφορικές εξισώσεις","Παρεμβολή","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0600"],"render_values":[{"text":"10.12681/eadd/0600","href":"https://doi.org/10.12681/eadd/0600","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/0600","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Ηροδότου-Έλληνα, Μαρίνα","Irodotou-Ellina, Marina"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1987"]},{"key":"dc:publisher","label":"Institution","values":["Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","Aristotle University Of Thessaloniki (AUTH)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Collocation","Differential equations","Interpolation","QUINTIC SPLINES","Διαφορικές εξισώσεις","Παρεμβολή","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","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/0600","http://hdl.handle.net/10442/hedi/0600"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE APPROXIMATION SOLUTIONS AREPIECEWISE POLYNOMIALS OF DEGREE 5, IN THE SPACE C4. WE MAKE A THEORETICAL STUDYING OF THESE METHODS AND WE PROVE THEIR OPTIMAL CONVERGENCE. WE ALSO PRESENT THE COMPUTATIONAL BEHAVIOUR OF THE OPTIMAL QUINTIC SPLINE COLLOCATION METHOD.","ΓΙΝΕΤΑΙ ΑΝΑΠΤΥΞΗ ΚΑΙ ΜΕΛΕΤΗ ΒΕΛΤΙΣΤΩΝ ΜΕΘΟΔΩΝ ΠΑΡΕΜΒΟΛΗΣ (COLLOCATION) ΓΙΑ ΤΗΝ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΗΣ ΓΡΑΜΜΙΚΩΝ ΚΑΙ ΜΗ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΔΕΥΤΕΡΟΥ ΚΑΙ ΤΕΤΑΡΤΟΥ ΒΑΘΜΟΥ ΕΛΛΕΙΠΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ. ΟΙ ΕΞΙΣΩΣΕΙΣ ΑΥΤΕΣ ΘΕΩΡΟΥΝΤΑΙ ΟΡΙΣΜΕΝΕΣ ΣΕ ΠΕΠΕΡΑΣΜΕΝΑ ΠΕΔΙΑ ΣΤΟΥΣ ΧΩΡΟΥΣ R KAI R2 ΚΑΙ Η ΛΥΣΗ ΤΟΥΣ ΙΚΑΝΟΠΟΙΕΙ ΟΡΙΣΜΕΝΕΣ ΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ. Η ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΗΣ ΤΩΝ ΓΙΝΕΤΑΙ ΜΕ ΤΜΗΜΑΤΙΚΑ ΠΟΛΥΩΝΥΜΑ ΒΑΘΜΟΥ 5 ΣΤΟ ΧΩΡΟ C4. ΓΙΝΕΤΑΙ ΑΝΑΛΥΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΤΕΤΟΙΩΝ ΜΕΘΟΔΩΝ ΚΑΙ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ Η ΣΥΓΚΛΙΣΗ ΤΩΝ ΜΕΘΟΔΩΝ ΕΙΝΑΙ ΒΕΛΤΙΣΤΗ ΩΣ ΠΡΟΣ ΤΗΝ ΣΥΜΠΕΡΙΦΟΡΑ ΤΟΥΣΦΑΛΜΑΤΟΣ ΠΑΡΕΜΒΟΛΗΣ ΣΥΝΑΡΤΗΣΕΩΝ ΣΤΟΝ ΙΔΙΟ ΧΩΡΟ ΤΜΗΜΑΤΙΚΩΝ ΠΟΛΥΩΝΥΜΩΝ. ΕΤΣΙ, ΣΥΝΟΠΤΙΚΑ ΣΤΗΝ ΔΙΔΑΚΤΟΡΙΚΗ ΑΥΤΗ ΔΙΑΤΡΙΒΗ ΑΠΕΔΕΙΧΘΗΚΕ ΥΠΑΡΞΗ ΒΕΛΤΙΣΤΩΝ ΠΕΠΕΡΑΣΜΕΝΩΝ ΣΤΟΙΧΕΙΩΝ ΠΡΟΣΕΓΓΙΣΕΩΝ ΤΥΠΟΥ COLLOCATION ΣΤΟ ΧΩΡΟ ΤΩΝ SPLINES ΠΕΜΠΤΟΥ ΒΑΘΜΟΥΓΙΑ ΕΛΛΕΙΠΤΙΚΑ ΠΡΟΒΛΗΜΑΤΑ."]},{"key":"dc:title","label":"Title","values":["ΜΕΘΟΔΟΙ ΠΑΡΕΜΒΟΛΗΣ ΜΕ Ο(Η6) ΣΥΓΚΛΙΣΗ ΓΙΑ ΕΛΛΕΙΠΤΙΚΕΣ ΕΞΙΣΩΣΕΙΣ 2ΗΣ ΚΑΙ 4ΗΣ ΤΑΞΗΣ","AN O(H6) COLLOCATION METHODS FOR SECOND AND FOURTH ORDER ELLIPTIC EQUATIONS"]}]}],"canonical_facts":{"dc:creator":["Ηροδότου-Έλληνα, Μαρίνα","Irodotou-Ellina, Marina"],"dc:date":["1987"],"dc:description":["IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE APPROXIMATION SOLUTIONS AREPIECEWISE POLYNOMIALS OF DEGREE 5, IN THE SPACE C4. WE MAKE A THEORETICAL STUDYING OF THESE METHODS AND WE PROVE THEIR OPTIMAL CONVERGENCE. WE ALSO PRESENT THE COMPUTATIONAL BEHAVIOUR OF THE OPTIMAL QUINTIC SPLINE COLLOCATION METHOD.","ΓΙΝΕΤΑΙ ΑΝΑΠΤΥΞΗ ΚΑΙ ΜΕΛΕΤΗ ΒΕΛΤΙΣΤΩΝ ΜΕΘΟΔΩΝ ΠΑΡΕΜΒΟΛΗΣ (COLLOCATION) ΓΙΑ ΤΗΝ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΗΣ ΓΡΑΜΜΙΚΩΝ ΚΑΙ ΜΗ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ ΔΕΥΤΕΡΟΥ ΚΑΙ ΤΕΤΑΡΤΟΥ ΒΑΘΜΟΥ ΕΛΛΕΙΠΤΙΚΩΝ ΕΞΙΣΩΣΕΩΝ. ΟΙ ΕΞΙΣΩΣΕΙΣ ΑΥΤΕΣ ΘΕΩΡΟΥΝΤΑΙ ΟΡΙΣΜΕΝΕΣ ΣΕ ΠΕΠΕΡΑΣΜΕΝΑ ΠΕΔΙΑ ΣΤΟΥΣ ΧΩΡΟΥΣ R KAI R2 ΚΑΙ Η ΛΥΣΗ ΤΟΥΣ ΙΚΑΝΟΠΟΙΕΙ ΟΡΙΣΜΕΝΕΣ ΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ. Η ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΗΣ ΤΩΝ ΓΙΝΕΤΑΙ ΜΕ ΤΜΗΜΑΤΙΚΑ ΠΟΛΥΩΝΥΜΑ ΒΑΘΜΟΥ 5 ΣΤΟ ΧΩΡΟ C4. ΓΙΝΕΤΑΙ ΑΝΑΛΥΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΤΕΤΟΙΩΝ ΜΕΘΟΔΩΝ ΚΑΙ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ Η ΣΥΓΚΛΙΣΗ ΤΩΝ ΜΕΘΟΔΩΝ ΕΙΝΑΙ ΒΕΛΤΙΣΤΗ ΩΣ ΠΡΟΣ ΤΗΝ ΣΥΜΠΕΡΙΦΟΡΑ ΤΟΥΣΦΑΛΜΑΤΟΣ ΠΑΡΕΜΒΟΛΗΣ ΣΥΝΑΡΤΗΣΕΩΝ ΣΤΟΝ ΙΔΙΟ ΧΩΡΟ ΤΜΗΜΑΤΙΚΩΝ ΠΟΛΥΩΝΥΜΩΝ. ΕΤΣΙ, ΣΥΝΟΠΤΙΚΑ ΣΤΗΝ ΔΙΔΑΚΤΟΡΙΚΗ ΑΥΤΗ ΔΙΑΤΡΙΒΗ ΑΠΕΔΕΙΧΘΗΚΕ ΥΠΑΡΞΗ ΒΕΛΤΙΣΤΩΝ ΠΕΠΕΡΑΣΜΕΝΩΝ ΣΤΟΙΧΕΙΩΝ ΠΡΟΣΕΓΓΙΣΕΩΝ ΤΥΠΟΥ COLLOCATION ΣΤΟ ΧΩΡΟ ΤΩΝ SPLINES ΠΕΜΠΤΟΥ ΒΑΘΜΟΥΓΙΑ ΕΛΛΕΙΠΤΙΚΑ ΠΡΟΒΛΗΜΑΤΑ."],"dc:identifier":["10.12681/eadd/0600","http://hdl.handle.net/10442/hedi/0600"],"dc:language":["gre"],"dc:publisher":["Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","Aristotle University Of Thessaloniki (AUTH)"],"dc:subject":["Collocation","Differential equations","Interpolation","QUINTIC SPLINES","Διαφορικές εξισώσεις","Παρεμβολή","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"dc:title":["ΜΕΘΟΔΟΙ ΠΑΡΕΜΒΟΛΗΣ ΜΕ Ο(Η6) ΣΥΓΚΛΙΣΗ ΓΙΑ ΕΛΛΕΙΠΤΙΚΕΣ ΕΞΙΣΩΣΕΙΣ 2ΗΣ ΚΑΙ 4ΗΣ ΤΑΞΗΣ","AN O(H6) COLLOCATION METHODS FOR SECOND AND FOURTH ORDER ELLIPTIC EQUATIONS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:21Z"}