Volterra型积分微分方程Chebyshev谱配置法求解

Volterra type integral-differential equations solution by Chebyshev spectral collocation method

采用Chebyshev谱配置法求解Volterra型积分微分方程.首先将积分微分方程改写成等价的第二类Volterra积分方程组,再取Clenshaw-Curtis点为配置点,然后利用Clenshaw-Curtis求积法则离散方程中积分项得到配置方程组,最后给出在L∞范数空间下的误差分析,并用数值实例验证理论分析的结果.该方法既有谱精度,程序又易实现.

The Chebyshev spectral collocation method is proposed to solve Volterra type integral-differential equations. Firstly, the integral-differential equation is rewritten into an equivalent system of Volterra integral equations of the second type, and Clenshaw-Curtis point is taken as the collocation point, then Clenshaw-Curtis quadrature rule is used to discretize the integral term in the equation to obtain the collocation equations, and finally the error analysis is conducted in L∞norm space and numerical examples are presented to verify the theoretical results. The method has spectral accuracy and is easy to implement.