Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations

2014/08/18 by D. Nazari Susahab, Susahab, D. Nazari, S. Shahmorad +1
Mathematics · #34A08 #65L60 #65R20 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1408.4029

openalex publication_date 2014/08/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

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