Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation
This study presents families of the fourth-order Runge–Kutta methods for solving a quadratic Riccati differential equation. From these families, the England version is more efficient than other fourth-order Runge–Kutta methods and practically well-suited for solving initial value problems in general...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2024-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2024/1433858 |
| _version_ | 1797234404194516992 |
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| author | Wendafrash Seyid Yirga Fasika Wondimu Gelu Wondwosen Gebeyaw Melesse Gemechis File Duressa |
| author_facet | Wendafrash Seyid Yirga Fasika Wondimu Gelu Wondwosen Gebeyaw Melesse Gemechis File Duressa |
| author_sort | Wendafrash Seyid Yirga |
| collection | DOAJ |
| description | This study presents families of the fourth-order Runge–Kutta methods for solving a quadratic Riccati differential equation. From these families, the England version is more efficient than other fourth-order Runge–Kutta methods and practically well-suited for solving initial value problems in general and quadratic Riccati differential equation in particular. The stability analysis of the present method is well-established. In order to verify the accuracy, we compared the numerical solutions obtained using the England version of fourth-order Runge–Kutta method with the recently published works reported in the literature. Several counter examples are solved using the present methods to demonstrate their reliability and efficiency. |
| first_indexed | 2024-04-24T16:31:31Z |
| format | Article |
| id | doaj.art-614cd254a3324764badee6a2d0ab917b |
| institution | Directory Open Access Journal |
| issn | 1687-0409 |
| language | English |
| last_indexed | 2024-04-24T16:31:31Z |
| publishDate | 2024-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj.art-614cd254a3324764badee6a2d0ab917b2024-03-30T00:00:01ZengHindawi LimitedAbstract and Applied Analysis1687-04092024-01-01202410.1155/2024/1433858Efficient Numerical Method for Solving a Quadratic Riccati Differential EquationWendafrash Seyid Yirga0Fasika Wondimu Gelu1Wondwosen Gebeyaw Melesse2Gemechis File Duressa3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThis study presents families of the fourth-order Runge–Kutta methods for solving a quadratic Riccati differential equation. From these families, the England version is more efficient than other fourth-order Runge–Kutta methods and practically well-suited for solving initial value problems in general and quadratic Riccati differential equation in particular. The stability analysis of the present method is well-established. In order to verify the accuracy, we compared the numerical solutions obtained using the England version of fourth-order Runge–Kutta method with the recently published works reported in the literature. Several counter examples are solved using the present methods to demonstrate their reliability and efficiency.http://dx.doi.org/10.1155/2024/1433858 |
| spellingShingle | Wendafrash Seyid Yirga Fasika Wondimu Gelu Wondwosen Gebeyaw Melesse Gemechis File Duressa Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation Abstract and Applied Analysis |
| title | Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation |
| title_full | Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation |
| title_fullStr | Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation |
| title_full_unstemmed | Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation |
| title_short | Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation |
| title_sort | efficient numerical method for solving a quadratic riccati differential equation |
| url | http://dx.doi.org/10.1155/2024/1433858 |
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