求解二次 Riccati 微分方程的高效数值方法

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2024-03-22 DOI:10.1155/2024/1433858

Wendafrash Seyid Yirga, Fasika Wondimu Gelu, Wondwosen Gebeyaw Melesse, G. Duressa

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引用次数: 0

摘要

本研究介绍了求解二次 Riccati 微分方程的四阶 Runge-Kutta 方法系列。与其他四阶 Runge-Kutta 方法相比，英格兰版本的四阶 Runge-Kutta 方法更为高效，实际上非常适合求解一般初值问题，尤其是二次 Riccati 微分方程。本方法的稳定性分析是成熟的。为了验证该方法的准确性，我们将使用英格兰版四阶 Runge-Kutta 方法获得的数值解与最近发表的文献报告进行了比较。为了证明本方法的可靠性和高效性，我们使用本方法求解了几个反例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 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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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important 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 material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.