Numerical methods for solution of Volterra and Fredholm integral equations for functions with values in L-spaces

Vira Babenko

Applied Mathematics and Computation, 2016, vol. 291, issue C, 354-372

Abstract: We consider Volterra and Fredholm integral equations for functions with values in L-spaces. This includes corresponding problems for set-valued functions, fuzzy-valued functions and many others. We prove theorems of existence and uniqueness of the solution for such equations and suggest some algorithms for finding approximate solutions. We get initial results in the approximation of functions with values in L-spaces by piecewise linear functions and we also get the error estimates of trapezoidal quadrature formulas. We apply these results for analysis of convergence of suggested algorithms.

Keywords: Volterra and Fredholm integral equations; L-space; Set-valued and fuzzy-valued functions; Algorithms; Approximation (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:291:y:2016:i:c:p:354-372

DOI: 10.1016/j.amc.2016.07.024

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