利用第二类Chebyshev小波求二阶常微分方程组边值问题的数值解  

Numerical Solutions for the Systems of Second-Order Boundary Value Problems Using the Second Kind Chebyshev Wavelets

作　　者：周凤英[1] 许小勇[1] 

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《数学的实践与认识》2016年第16期242-252,共11页Mathematics in Practice and Theory

基　　金：江西省自然科学基金(20151BAB211004);江西省自然科学基本项目(2015BAB211012);国家自然科学基金(11561002)

摘　　要：给出了一个求二阶常微分方程组边值问题数值解的第二类Chebyshev小波配点法.利用第二类Chebyshev小波积分算子矩阵,将问题转化成代数方程组的运算.数值例子说明了方法的准确性及易操作性.另外,为了表明方法的高精度性和有效性,数值算例结果与解析解,以及运用变分迭代法,B样条配点法,连续遗传算法等得到的结果进行了比较.In this paper, a collocation method based on the second kind Chebyshev wavelets is presented for the numerical solutions of the systems of second-order boundary value problems. Integral operator matrix of the second kind Chebyshev wavelets is used to reduce the computation of the solutions for this systems to some algebraic equations. Some numerical examples are studied to demonstrate the accuracy and easy implementation of the technique. In order to show the accuracy and efficiency of the proposed approach, numerical experiment results are compared with the analytical solutions, variational iteration method, B-spline collocation method, continuous genetic algorithm and some published methods.

关 键 词：第二类Chebyshev小波 二阶常微分方程组边值问题 积分算子矩阵 配点法 

分 类 号：O241.81[理学—计算数学]