Modified Euler’s method with a graded mesh for a class of Volterra integral equations with weakly singular kernel

A modified Euler’s method applied on a graded mesh is considered for numerical solution of a class of Volterra integral equations with weakly singular kernel which depends on a parameter μ > 0. It is shown that the convergence rate of the considered method is higher than those of earlier ones for...

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Vydáno v:Numerical algorithms Ročník 67; číslo 2; s. 405 - 422
Hlavní autor: Majidian, Hassan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.10.2014
Springer Nature B.V
Témata:
Algebra
Algorithms
Computer Science
Convergence
Kernels
Mathematical models
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Volterra integral equations
Primary 65R20
Volterra integral equation
Euler’s method
Graded mesh
Singular kernel
ISSN:1017-1398, 1572-9265
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Shrnutí:A modified Euler’s method applied on a graded mesh is considered for numerical solution of a class of Volterra integral equations with weakly singular kernel which depends on a parameter μ > 0. It is shown that the convergence rate of the considered method is higher than those of earlier ones for the case when μ ≤ 1. The convergence rate is also obtained in the case μ > 1. Using some numerical examples, we illustrate the theoretical results.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-013-9799-3