Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

作者：Yang Yin; Chen Yanping^*; Huang Yunqing; Yang Wei

来源：ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2015, 7(1): 74-88.

DOI：10.4208/aamm.2013.m163

• Spectral method
• nonlinear
• Volterra integral equations

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors in L-2-norm and L-infinity-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.

• 单位
  华南师范大学; 湘潭大学