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.

Wendafrash Seyid Yirga

Fasika Wondimu Gelu

Wondwosen Gebeyaw Melesse

Gemechis File Duressa

Abstract and Applied Analysis

ABSTRACT AND APPLIED ANALYSIS 是一本专门致力于发表抽象和应用分析领域的高质量研究论文的数学期刊。重点放在经典分析、线性和非线性泛函分析、常微分方程和偏微分方程、优化理论和控制理论方面的重要发展。摘要和应用分析支持出版涉及上述学科重大问题的完整解决方案的原始材料。摘要和应用分析还鼓励就分析理论和应用的当前趋势发表及时而全面的调查文章。

Abstract and Applied Analysis is a mathematical journal dedicated to publishing high-quality research papers in the field of abstract and applied analysis. The journal focuses on significant developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original materials that provide comprehensive solutions to major problems in these disciplines. Additionally, the journal encourages timely and comprehensive survey articles on current trends in analysis theory and applications.

《Abstract and Applied Analysis》是一本专注于发表抽象与应用分析领域高质量研究论文的数学期刊。期刊重点关注经典分析、线性与非线性泛函分析、常微分方程与偏微分方程、优化理论及控制理论等领域的重要发展。《Abstract and Applied Analysis》支持发表涉及上述学科重大问题的完整解决方案的原创研究材料。同时，期刊也鼓励发表关于分析理论与应用当前趋势的及时而全面的综述文章。

Efficient Numerical Method for Solving a Quadratic Riccati Differential Equation

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