[1]胡凯丽,李岩.基于符号计算的BBM方程的精确解[J].计算机技术与发展,2019,29(05):70-73.[doi:10. 3969 / j. issn. 1673-629X. 2019. 05. 015]
　HU Kai-li,LI Yan.Exact Solution of BBM Equation Based on Symbolic Computation[J].,2019,29(05):70-73.[doi:10. 3969 / j. issn. 1673-629X. 2019. 05. 015]
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基于符号计算的BBM方程的精确解()
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《计算机技术与发展》[ISSN:1006-6977/CN:61-1281/TN]

卷:
29
期数:
2019年05期
页码:
70-73
栏目:
智能、算法、系统工程
出版日期:
2019-05-10

文章信息/Info

Title:
Exact Solution of BBM Equation Based on Symbolic Computation
文章编号:
1673-629X(2019)05-0070-04
作者:
胡凯丽; 李岩
陕西师范大学 计算机科学学院,陕西 西安 710119
Author(s):
HU Kai-li; LI Yan
School of Computer Science,Shaanxi Normal University,Xi’an 710119,China
关键词:
计算机代数; Benjamin-Bona-Mahony 方程;  (G’/ G2) -展开法; 精确解
Keywords:
computer algebra; Benjamin-Bona-Mahony equation;  (G’/ G2) -expansion method; exact solution
分类号:
TP31
DOI:
10. 3969 / j. issn. 1673-629X. 2019. 05. 015
摘要:
符号计算又称计算机代数,是涉及数学、计算机科学和人工智能的新兴交叉学科,研究如何在计算机上进行符号演算和自动推理,是数学机械化的主要工具。 常用的符号计算系统主要有 Maple、Mathematica、REDUCE 等。 非线性偏微分方程可以真实准确地描述客观世界中的自然现象,因此求解非线性偏微分方程精确解具有非常重要的意义。 近年来,随着各种求解方法的不断出现,过去难以求解的方程得到了解决,尤其是借助符号计算系统,复杂的求解过程变得更加简洁快速。 文中借助符号计算系统 Maple,利用 (G’/ G2) -展开法求解 Benjamin-Bona-Mahony 方程,得到了方程的三角函数通解、双曲函数通解以及有理函数通解。 特别地,当双曲函数通解中的常数取特殊值时,得到了方程的孤立波解。 研究结果表明, (G’/ G2) -展开法简洁高效,适用于其他非线性偏微分方程。
Abstract:
Symbolic computation,also known as computer algebra, is a new interdisciplinary subject involving mathematics, computer science and artificial intelligence. It studies how to perform symbolic computation and automatic reasoning on computers and is the main tool of mathematical mechanization. The common symbolic computation systems include Maple,Mathematica,REDUCE and so on. The nonlinear partial differential equation can describe the natural phenomena in the objective world truly and accurately. Therefore,it is very important to solve the exact solution of the nonlinear partial differential equation. In recent years,with the continuous emergence of various solution methods,the equations which are difficult to solve in the past have been solved,especially with the aid of symbolic computing system,the complex solution process becomes more concise and rapid. With the help of symbolic computation system Maple,the (G’/ G2) -expansion method is used to solve the Benjamin-Bona-Mahony equation for the general solution of the trigonometric function,the hyperbolic function and the rational function. In particular,when the constants in the general solution of hyperbolic functions are given special values, the solitary wave solutions of the equations are obtained. The results show that the (G’/ G2) - expansion method,which is simple and efficient,is suitable for other nonlinear partial differential equations.
更新日期/Last Update: 2019-05-10