非线性第二类Volterra积分方程的Chebyshev谱配置法

CHEBYSHEV SPECTRAL COLLOCATION METHOD FOR NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND

我们在参考了相关文献的基础上,考察了一类非线性Volterra积分方程的Chebyshev谱配置法.方法中,我们将该类非线性方程转化为两个方程进行数值逼近.我们选择N阶Chebyshev Gauss-Lobatto点作为配置点,对积分项用N阶高斯数值积分公式逼近.收敛性分析结果表明数值误差的收敛阶为N^(1/2)-m,其中m是已知函数最高连续导数的阶数.我们也开展数值实验证实这一理论分析结果.

Base on related references,we investigate the Chebyshev spectral collocation method for nonlinear Volterra integral equations of the second kind.The main idea of the presented method is to approximate numerically the new equations which are tranformedfrom the nonlinear Volterra integral equations of the second kind.The collocation points are Chebyshev Gauss-Lobatto points of order N.The integral terms are approximated by Gauss quadrature formula of order N.The provided convergence analysis shows thatthe convergence rate of the numerical errors is N^(1/2)-m provided that the given functions are m times continuous differentiable.This theoretical result is confirmed by the provided numerical experiments.