Volterra型积分微分方程Chebyshev谱配置法求解

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方春华,黄超兰,王建雨.Volterra型积分微分方程Chebyshev谱配置法求解[J].,2023,63(2):215-220

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

DOI：10.7511/dllgxb202302013

中文关键词:Volterra型积分微分方程第二类Volterra积分方程组 Chebyshev谱配置法 Clenshaw-Curtis求积谱精度

英文关键词:Volterra type integral-differential equation Volterra integral equations of the second kind Chebyshev spectral collocation method Clenshaw-Curtis quadrature spectral accuracy

基金项目:湖南省自然科学基金资助项目(2022JJ30276).

作者	单位
方春华,黄超兰,王建雨

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中文摘要:

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．

英文摘要:

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.

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Volterra型积分微分方程Chebyshev谱配置法求解

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