Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations
arXiv:1408.40291.21 citations
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Provides numerical methods for solving weakly singular integral equations, which are important for fractional differential equations, but the contribution appears incremental.
The paper develops multistep collocation methods for weakly singular Volterra integral equations, achieving convergence orders and superconvergence, with application to fractional differential equations.
We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-τ)^{α-1}$ with $0 <α<1.$ Convergence orders of the methods are determined and their superconvergence is also analyzed. The paper closes with numerical examples and application to fractional differential equations.