Convergence analysis of spectral collocation methods for a class of weakly singular Volterra integral equations
作者： Xiaohua Ma , Chengming Huang , Xin Niu
DOI: 10.1016/J.AMC.2014.10.100
关键词: Standard interval 、 Error analysis 、 Singular integral 、 Spectral collocation 、 Integral equation 、 Source function 、 Mathematics 、 Quadrature (mathematics) 、 Volterra integral equation 、 Mathematical analysis
摘要: Abstract In this paper, we discuss the application of spectral Jacobi-collocation methods to a certain class weakly singular Volterra integral equations. First, use some function transformations and variable changes transform equation into defined on standard interval [ - 1 , ] . Then Jacobi–Gauss quadrature formula is used approximate operator. For method, rigorous error analysis in both L ∞ weighted 2 norms given under assumption that kernel source are sufficiently smooth. Finally, numerical examples provided illustrate theoretical results.
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