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 |
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Hindawi Limited
2024-01-01
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Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2024/1433858 |
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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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