STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
This paper presents the stability analysis of a proposed scheme of order five (FCM) for first order Ordinary Differential Equations (ODEs). The proposed FCM is derived by means of an interpolating function of polynomial and exponential forms. The properties of FCM were discussed extensively. The lin...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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UiTM Press
2021-09-01
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| Series: | Malaysian Journal of Computing |
| Subjects: |
| _version_ | 1797450753347944448 |
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| author | Sunday Emmanuel Fadugba Roseline Bosede Ogunrinde Rowland Rotimi Ogunrinde |
| author_facet | Sunday Emmanuel Fadugba Roseline Bosede Ogunrinde Rowland Rotimi Ogunrinde |
| author_sort | Sunday Emmanuel Fadugba |
| collection | DOAJ |
| description | This paper presents the stability analysis of a proposed scheme of order five (FCM) for first order Ordinary Differential Equations (ODEs). The proposed FCM is derived by means of an interpolating function of polynomial and exponential forms. The properties of FCM were discussed extensively. The linear stability of FCM in the context of the Third Order One-Step Method (TCM) and Second Order One-Step Method (SCM) for the solution of initial value problems of first order differential equations is presented. The stability region of FCM, TCM and SCM is investigated using the Dahlquist’s test equation. The numerical results obtained via FCM are compared with TCM and SCM. Moreover, by varying the step length, the accuracy and convergence of the methods in terms of the final absolute relative error are measured. The results show that FCM converges faster and more stable than its counterparts. |
| first_indexed | 2024-03-09T14:45:08Z |
| format | Article |
| id | doaj.art-18eabf7cdf7f46ecbb35961d5c4c9ddf |
| institution | Directory Open Access Journal |
| issn | 2600-8238 |
| language | English |
| last_indexed | 2024-03-09T14:45:08Z |
| publishDate | 2021-09-01 |
| publisher | UiTM Press |
| record_format | Article |
| series | Malaysian Journal of Computing |
| spelling | doaj.art-18eabf7cdf7f46ecbb35961d5c4c9ddf2023-11-27T07:11:02ZengUiTM PressMalaysian Journal of Computing2600-82382021-09-0162898912https://doi.org/10.24191/mjoc.v6i2.9756STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONSSunday Emmanuel Fadugba0Roseline Bosede Ogunrinde1Rowland Rotimi Ogunrinde2Ekiti State UniversityEkiti State UniversityAugustine UniversityThis paper presents the stability analysis of a proposed scheme of order five (FCM) for first order Ordinary Differential Equations (ODEs). The proposed FCM is derived by means of an interpolating function of polynomial and exponential forms. The properties of FCM were discussed extensively. The linear stability of FCM in the context of the Third Order One-Step Method (TCM) and Second Order One-Step Method (SCM) for the solution of initial value problems of first order differential equations is presented. The stability region of FCM, TCM and SCM is investigated using the Dahlquist’s test equation. The numerical results obtained via FCM are compared with TCM and SCM. Moreover, by varying the step length, the accuracy and convergence of the methods in terms of the final absolute relative error are measured. The results show that FCM converges faster and more stable than its counterparts.fifth order schemefinal absolute relative errorinitial value problemsecond order methodstabilitythird order method |
| spellingShingle | Sunday Emmanuel Fadugba Roseline Bosede Ogunrinde Rowland Rotimi Ogunrinde STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS Malaysian Journal of Computing fifth order scheme final absolute relative error initial value problem second order method stability third order method |
| title | STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS |
| title_full | STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS |
| title_fullStr | STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS |
| title_full_unstemmed | STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS |
| title_short | STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS |
| title_sort | stability analysis of a proposed scheme of order five for first order ordinary differential equations |
| topic | fifth order scheme final absolute relative error initial value problem second order method stability third order method |
| work_keys_str_mv | AT sundayemmanuelfadugba stabilityanalysisofaproposedschemeoforderfiveforfirstorderordinarydifferentialequations AT roselinebosedeogunrinde stabilityanalysisofaproposedschemeoforderfiveforfirstorderordinarydifferentialequations AT rowlandrotimiogunrinde stabilityanalysisofaproposedschemeoforderfiveforfirstorderordinarydifferentialequations |