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 |
| Summary: | 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. |
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| ISSN: | 1687-0409 |