基于计算机代数法求解非线性动力系统.doc

毕 业 论 文 专 业： 数学与应用数学 班级学号： 学生姓名： 指导教师： 二〇XX年X月 XXXX大学本科生毕业论文 基于计算机代数法求解非线性动力系统 A method based on the Computer Algebra for solving the Non-linearity Dynamic System 专业班级： 学生姓名： 指导教师： 学 院： 20XX年 X 月 摘 要 本课题主要研究计算机代数法(Computer Algebra method)在微分方程中的应用。计算机代数法提供了些方法，使得微分方程能得到更多精确解。首先是对计算机代数法的一些基本知识做了介绍，这些基本的知识为下面接下来的研究打下一定的基础。基于计算机代数法分析，讨论了三维拓展量子ZK方程,可变广义Vaknenko方程，PHI-four方程。其中，首先将解拟似成代数的形式，然后代入原方程中，令未知量的系数为零，来确定解的形式。例如在求解ZK方程时，利用四种不同的拟似解来求得了多种形式的解，包括双周期波，孤立波，震动波，有理波，和奇异波解。经过尝试，利用计算机代数法来求解可变广义Vaknenko方程，PHI-four方程，也得到了更多的精确解，从而证明了该方法是一种非常有效的求解非线性方程的方法。 关键词：微分方程；计算机代数法；拟似；精确解 ABSTRACT This topic research Computer algebraic method (Computer Algebra in differential equation of the application. Computer algebraic method provides some methods, making the differential equation can get more precise solution. First the computer algebra some basic knowledge of law, was introduced these basic knowledge in the subsequent research provides a basis. Based on computer algebra method analysis, we discussed the three-dimensional quantum ZK equation, variable expand Vaknenko equation, generalized PHI - four equations. Among them, will first solution into algebra form to like, then generation into the original equation, making the coefficient of unknown variables zero, to determine the form of solution. For example in solving ZK equation, we used four differential equations to the various forms for the solution, including double a periodic wave, solitary wave, shock waves, rational wave, and singular wave solutions. After trying, the computer algebraic method to solve variable Vaknenko equation, generalized PHI - four equations, also got more exact solutions, which proves that the method is a very effective method of solving nonlinear equations. Key Words： Differential Equations; Computer Algebra Method; Generalized Ans?tz; Exact Solutions 目 录 1 绪 论 1 1.1 课题研究背景 1 1.2 课题研究意义 2 2 计算机代数法的介绍 3 2.1 雅可比的线性函数 3 2.2 雅可