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Trigonometrically fitted multistep methods for solving oscillatory problems

At the beginning of the thesis, we trigonometrically fitted the first point of the existing block multistep method which was purposely derived for solving special second order ordinary differential equations (ODEs). Based on the original multistep method, we construct both explicit and implici...

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محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Mansor, Aini Fadhlina
التنسيق: أطروحة
اللغة:English
منشور في: 2017
الوصول للمادة أونلاين:http://psasir.upm.edu.my/id/eprint/69418/1/IPM%202018%201%20IR.pdf
http://psasir.upm.edu.my/id/eprint/69418/
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id my.upm.eprints.69418
record_format eprints
spelling my.upm.eprints.694182019-07-10T00:59:03Z http://psasir.upm.edu.my/id/eprint/69418/ Trigonometrically fitted multistep methods for solving oscillatory problems Mansor, Aini Fadhlina At the beginning of the thesis, we trigonometrically fitted the first point of the existing block multistep method which was purposely derived for solving special second order ordinary differential equations (ODEs). Based on the original multistep method, we construct both explicit and implicit trigonometrically fitted multistep methods of step number k=4 and develop code using both constant and variable step size. The trigonometrically fitting technique has been applied to the original method in order to construct the new methods. The numerical results show that the trigonometrically fitted multistep method is more efficient compared to the existing methods in solving special second order ordinary differential equations (ODEs) which are oscillatory in nature. Then, the 2-point explicit and implicit block multistep methods of step number k=3 and k=5 for solving special second order ODEs are derived using integration formula based on Newton-Gregory backward interpolation polynomial. The methods are implemented for constant step size by using the predictor-corrector technique, followed by the implementation using variable step size. The numerical results are given to show the efficiency of the new methods as compared to the existing methods. The 2-point explicit and implicit block multistep methods of step number k=3 and k=5 are then trigonometrically fitted so that they are suitable for solving special second order ordinary differential equations, which are highly oscillatory in nature. We developed codes based on the trigonometrically fitted methods using constant step size in predictor-corrector mode. The numerical results obtained show that trigonometrically fitted the methods give more accurate solutions than the existing methods. In conclusion, trigonometrically fitted block and non-block multistep methods have been derived in this thesis for solving oscillatory problems. The illustrative examples are given in the form of both tables and graphs which clearly shown the advantage of the methods. 2017-12 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/69418/1/IPM%202018%201%20IR.pdf Mansor, Aini Fadhlina (2017) Trigonometrically fitted multistep methods for solving oscillatory problems. Masters thesis, Universiti Putra Malaysia.
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description At the beginning of the thesis, we trigonometrically fitted the first point of the existing block multistep method which was purposely derived for solving special second order ordinary differential equations (ODEs). Based on the original multistep method, we construct both explicit and implicit trigonometrically fitted multistep methods of step number k=4 and develop code using both constant and variable step size. The trigonometrically fitting technique has been applied to the original method in order to construct the new methods. The numerical results show that the trigonometrically fitted multistep method is more efficient compared to the existing methods in solving special second order ordinary differential equations (ODEs) which are oscillatory in nature. Then, the 2-point explicit and implicit block multistep methods of step number k=3 and k=5 for solving special second order ODEs are derived using integration formula based on Newton-Gregory backward interpolation polynomial. The methods are implemented for constant step size by using the predictor-corrector technique, followed by the implementation using variable step size. The numerical results are given to show the efficiency of the new methods as compared to the existing methods. The 2-point explicit and implicit block multistep methods of step number k=3 and k=5 are then trigonometrically fitted so that they are suitable for solving special second order ordinary differential equations, which are highly oscillatory in nature. We developed codes based on the trigonometrically fitted methods using constant step size in predictor-corrector mode. The numerical results obtained show that trigonometrically fitted the methods give more accurate solutions than the existing methods. In conclusion, trigonometrically fitted block and non-block multistep methods have been derived in this thesis for solving oscillatory problems. The illustrative examples are given in the form of both tables and graphs which clearly shown the advantage of the methods.
format Thesis
author Mansor, Aini Fadhlina
spellingShingle Mansor, Aini Fadhlina
Trigonometrically fitted multistep methods for solving oscillatory problems
author_facet Mansor, Aini Fadhlina
author_sort Mansor, Aini Fadhlina
title Trigonometrically fitted multistep methods for solving oscillatory problems
title_short Trigonometrically fitted multistep methods for solving oscillatory problems
title_full Trigonometrically fitted multistep methods for solving oscillatory problems
title_fullStr Trigonometrically fitted multistep methods for solving oscillatory problems
title_full_unstemmed Trigonometrically fitted multistep methods for solving oscillatory problems
title_sort trigonometrically fitted multistep methods for solving oscillatory problems
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/69418/1/IPM%202018%201%20IR.pdf
http://psasir.upm.edu.my/id/eprint/69418/
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score 13.251813

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