Rational solutions of Riccati differential equation with coefficients rational

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• 作者：Nadhem Echi ^{nadhemechi_fsg@yahoo.fr}
• 关键词：Riccati differential equation with coefficients rational ; Second-order linear ordinary differential equation ; Taylor&rsquo ; s expansion ; Partial fraction decomposition
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 July, 2012
• 卷：218
• 期：21
• 页码：10341-10366
• 文件大小：369 K

摘要

This paper presents a simple and efficient method for determining the rational solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation , is reducible, we look for the rational solutions of Riccati differential equation , by reducing the number of check to be made and by accelerating the search for the partial fraction decomposition of the solution reserved for the poles of 胃 which are false poles of r. This partial fraction decomposition of solution can be used to code r. The examples demonstrate the effectiveness of the method.