High order product integration methods for a Volterra integral equation with logarithmic singular kernel | Zendy

Teresa Diogo | Zendy; Neide Bertoldi Franco | Zendy; Pedro M. Lima | Zendy

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High order product integration methods for a Volterra integral equation with logarithmic singular kernel

Author(s) -

Teresa Diogo,

Neide Bertoldi Franco,

Pedro M. Lima

Publication year - 2004

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2004.3.217

Subject(s) - volterra integral equation , logarithm , mathematics , convergence (economics) , kernel (algebra) , product (mathematics) , integral equation , order (exchange) , mathematical analysis , numerical integration , pure mathematics , geometry , finance , economics , economic growth

This work is concerned with the construction and analysis of high order product integration methods for a class of Volterra integral equations with logarithmic singular kernel. Sucient conditions for the methods to be convergent are derived and it is shown that optimal convergence orders are attained if the exact solution is suciently smooth. The case of non-smooth solutions is dealt with by making suitable transformations so that the new equation possesses smooth solutions. Two particular methods are considered and their convergence proved. A sample of numerical examples is included.

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