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2024 | OriginalPaper | Chapter

Kantorovich Methods for Urysohn Integral Equations

Authors : M. Arrai, C. Allouch, M. Tahrichi

Published in: Applied Mathematics and Modelling in Finance, Marketing and Economics

Publisher: Springer Nature Switzerland

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Abstract

In this paper, the Kantorovich method for the numerical solution of nonlinear Urysohn equations with a smooth kernel is considered. The approximating operator is chosen to be either the orthogonal projection or an interpolatory projection onto a space of piecewise polynomials of degree \(\le r-1\). This method have asymptotic series expansions and the orders of convergence can be further improved by the Richardson extrapolation, assuming the calculation to be repeated with each subinterval halved. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by calculating the integrals with a numerical quadrature formula. Numerical examples are given to illustrate the theoretical estimates.

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previous chapter Dynamic and Static Simulated Annealing for Solving the Multi-objective k-Minimum Spanning Tree Problem
next chapter The Maximal Numerical Range of a Quadratic Matrix
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Metadata
Title
Kantorovich Methods for Urysohn Integral Equations
Authors
M. Arrai
C. Allouch
M. Tahrichi
Copyright Year
2024
Book
Applied Mathematics and Modelling in Finance, Marketing and Economics

Print ISBN: 978-3-031-42846-3

Electronic ISBN: 978-3-031-42847-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-42847-0_5

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