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Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation

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Listed:
  • Wendafrash Seyid Yirga
  • Fasika Wondimu Gelu
  • Wondwosen Gebeyaw Melesse
  • Gemechis File Duressa

Abstract

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.

Suggested Citation

  • Wendafrash Seyid Yirga & Fasika Wondimu Gelu & Wondwosen Gebeyaw Melesse & Gemechis File Duressa, 2024. "Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).
    • Handle: RePEc:wly:jnlaaa:v:2024:y:2024:i:1:n:1433858
    DOI: 10.1155/2024/1433858
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    References listed on IDEAS

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    1. A. R. Vahidi & M. Didgar & R. C. Rach, 2014. "An improved approximate analytic solution for Riccati equations over extended intervals," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(1), pages 27-38, February.
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