Department of Mathematics
Convergence analysis of spectral galerkin methods for volterra type integral equations
This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a rigorous error analysis in both the infinity and weighted norms is given provided that both the kernel function and the source function are sufficiently smooth. Numerical experiments validate the theoretical prediction. © Springer Science+Business Media, LLC 2012.
Pseudo-spectral Galerkin, Spectral convergence, Spectral Galerkin, The second kind Volterra integral equations
Source Publication Title
Journal of Scientific Computing
Link to Publisher's Edition
Xie, Z., Li, X., & Tang, T. (2012). Convergence analysis of spectral galerkin methods for volterra type integral equations. Journal of Scientific Computing, 53 (2), 414-434. https://doi.org/10.1007/s10915-012-9577-8