A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves
Numerical methods are frequently developed to investigate concepts for approximately solving ordinary differential equations (ODEs). To achieve minimal error and higher accuracy in approximate solutions, researchers have focused on developing algorithms using various numerical techniques. This study...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/250 |
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| author | Abdul Hadi Bhatti Sharmila Karim Ala Amourah Ali Fareed Jameel Feras Yousef Nidal Anakira |
| author_facet | Abdul Hadi Bhatti Sharmila Karim Ala Amourah Ali Fareed Jameel Feras Yousef Nidal Anakira |
| author_sort | Abdul Hadi Bhatti |
| collection | DOAJ |
| description | Numerical methods are frequently developed to investigate concepts for approximately solving ordinary differential equations (ODEs). To achieve minimal error and higher accuracy in approximate solutions, researchers have focused on developing algorithms using various numerical techniques. This study proposes the application of Ball curves, specifically the Said–Ball curve, for estimating solutions to higher-order ODEs. To obtain the best control points of the Said–Ball curve, the least squares method is used. These control points are calculated by minimizing the residual error through the sum of the squares of the residual functions. To demonstrate the proposed method, several boundary value problems are presented, and their performance is compared with existing methods in terms of error accuracy. The numerical results indicate that the proposed method improves error accuracy compared to existing studies, including those employing Bézier curves and the steepest descent method. |
| format | Article |
| id | doaj-art-d63d3e26ab554ff4b14783d2a7c1735a |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d63d3e26ab554ff4b14783d2a7c1735a2025-01-24T13:39:54ZengMDPI AGMathematics2227-73902025-01-0113225010.3390/math13020250A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball CurvesAbdul Hadi Bhatti0Sharmila Karim1Ala Amourah2Ali Fareed Jameel3Feras Yousef4Nidal Anakira5Department of Mathematics and Applied Sciences, Middle East College, Muscat 124, OmanSchool of Quantitative Sciences, University Utara Malaysia, Sintok 06010, Kedah, MalaysiaMathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, OmanMathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, OmanDepartment of Mathematics, The University of Jordan, Amman 11942, JordanMathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, OmanNumerical methods are frequently developed to investigate concepts for approximately solving ordinary differential equations (ODEs). To achieve minimal error and higher accuracy in approximate solutions, researchers have focused on developing algorithms using various numerical techniques. This study proposes the application of Ball curves, specifically the Said–Ball curve, for estimating solutions to higher-order ODEs. To obtain the best control points of the Said–Ball curve, the least squares method is used. These control points are calculated by minimizing the residual error through the sum of the squares of the residual functions. To demonstrate the proposed method, several boundary value problems are presented, and their performance is compared with existing methods in terms of error accuracy. The numerical results indicate that the proposed method improves error accuracy compared to existing studies, including those employing Bézier curves and the steepest descent method.https://www.mdpi.com/2227-7390/13/2/250ordinary differential equationshigher ordererror accuracySaid–Ball curvecontrol pointsleast squares method |
| spellingShingle | Abdul Hadi Bhatti Sharmila Karim Ala Amourah Ali Fareed Jameel Feras Yousef Nidal Anakira A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves Mathematics ordinary differential equations higher order error accuracy Said–Ball curve control points least squares method |
| title | A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves |
| title_full | A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves |
| title_fullStr | A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves |
| title_full_unstemmed | A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves |
| title_short | A Novel Approximation Method for Solving Ordinary Differential Equations Using the Representation of Ball Curves |
| title_sort | novel approximation method for solving ordinary differential equations using the representation of ball curves |
| topic | ordinary differential equations higher order error accuracy Said–Ball curve control points least squares method |
| url | https://www.mdpi.com/2227-7390/13/2/250 |
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