第二类Volterra型积分方程的Chebyshev-Legendre谱配置方法  

Chebyshev-Legendre spectral collocation method for second kind Volterra integral equations

作　　者：吴华[1] 徐玲芳[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2014年第2期175-188,共14页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11171209);国家留学基金委科研启动基金资助项目;上海市教育委员会重点学科建设资助项目(J50101)

摘　　要：提出了一种新的求解第二类线性Volterra型积分方程的Chebyshev谱配置方法.该方法分别对方程中积分部分的核函数和未知函数在Chebyshev-Gauss-Lobatto点上进行插值,通过Chebyshev-Legendre变换,把插值多项式表示成Legendre级数形式,从而将积分转换为内积的形式,再利用Legendre多项式的正交性进行计算.利用Chebyshev插值算子在不带权范数意义下的逼近结果,对该方法在理论上给出了L∞范数意义下的误差估计,并通过数值算例验证了算法的有效性和理论分析的正确性.A new Chebyshev spectral collocation method is developed for the linear Volterra integral equations of the second kind. For the integral term of the equation, the kernel function and the unknown function are approximated by the Chebyshev-Gauss-Lobatto interpolation. Then, by using the Chebyshev-Legendre transforms, the form of the Legendre polynomials is obtained. Therefore, the integral form can be written into the inner-product form. The computation can also be simplified due to the orthogonality of the Legendre polynomials. The error estimation is obtained in the L^∞-norm. The numerical examples are provided to confirm the validity of the method and the correctness of the theoretical analysis.

关 键 词：第二类Volterra型积分方程 Chebyshev-Legendre谱配置方法 收敛性分析 

分 类 号：O241.83[理学—计算数学]