New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency
In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate t...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/6650855 |
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| _version_ | 1832551664981114880 |
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| author | Abushet Hayalu Workie |
| author_facet | Abushet Hayalu Workie |
| author_sort | Abushet Hayalu Workie |
| collection | DOAJ |
| description | In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate the conclusion, the stability, consistency, and accuracy of the system were evaluated and numerical results were presented, and it was recognized that the proposed method is more stable, consistent, and accurate with high performance. |
| format | Article |
| id | doaj-art-4732ea6cbae74b449050e2235bbd7bf9 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4732ea6cbae74b449050e2235bbd7bf92025-02-03T06:00:49ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/66508556650855New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High EfficiencyAbushet Hayalu Workie0Department of Mathematics, College of Natural and Computational Science, Debre Berhan University, Debre Berhan, EthiopiaIn this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate the conclusion, the stability, consistency, and accuracy of the system were evaluated and numerical results were presented, and it was recognized that the proposed method is more stable, consistent, and accurate with high performance.http://dx.doi.org/10.1155/2020/6650855 |
| spellingShingle | Abushet Hayalu Workie New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency Journal of Mathematics |
| title | New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency |
| title_full | New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency |
| title_fullStr | New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency |
| title_full_unstemmed | New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency |
| title_short | New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency |
| title_sort | new modification on heun s method based on contraharmonic mean for solving initial value problems with high efficiency |
| url | http://dx.doi.org/10.1155/2020/6650855 |
| work_keys_str_mv | AT abushethayaluworkie newmodificationonheunsmethodbasedoncontraharmonicmeanforsolvinginitialvalueproblemswithhighefficiency |