@Article{AAMM-4-1, author = {Yunxia, Wei and Yanping, Chen}, title = {Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {1}, pages = {1--20}, abstract = {

The theory of a class of spectral methods is extended to Volterra integro-differential equations which contain a weakly singular kernel $(t-s)^{-\mu}$ with $0<\mu<1$. In this work, we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth. We provide a rigorous error analysis for the spectral methods, which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in $L^\infty$-norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1055}, url = {https://global-sci.com/article/73526/convergence-analysis-of-the-spectral-methods-for-weakly-singular-volterra-integro-differential-equations-with-smooth-solutions} }