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Numerical Solution of Two-Dimensional Fredholm–Volterra Integral Equations of the Second Kind
- Source :
- Symmetry, Volume 13, Issue 8, Symmetry, Vol 13, Iss 1326, p 1326 (2021)
- Publication Year :
- 2021
- Publisher :
- Multidisciplinary Digital Publishing Institute, 2021.
-
Abstract
- The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations of the second kind. As these equations arise in many applications, there is a constant need for accurate, but fast and simple to use numerical approximations to their solutions. The method proposed here uses successive approximations of the Mann type and a suitable cubature formula. Mann’s procedure is known to converge faster than the classical Picard iteration given by the contraction principle, thus yielding a better numerical method. The existence and uniqueness of the solution is derived under certain conditions. The convergence of the method is proved, and error estimates for the approximations obtained are given. At the end, several numerical examples are analyzed, showing the applicability of the proposed method and good approximation results. In the last section, concluding remarks and future research ideas are discussed.
- Subjects :
- Physics and Astronomy (miscellaneous)
General Mathematics
Numerical analysis
010102 general mathematics
numerical approximations
010103 numerical & computational mathematics
01 natural sciences
Volterra integral equation
Integral equation
symbols.namesake
Chemistry (miscellaneous)
Fixed-point iteration
Convergence (routing)
Computer Science (miscellaneous)
symbols
QA1-939
Applied mathematics
Uniqueness
0101 mathematics
Contraction principle
Fredholm–Volterra integral equations
Constant (mathematics)
Mathematics
fixed-point theorems
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....fa851ee8655f355501b8f1bcc8d8cde2
- Full Text :
- https://doi.org/10.3390/sym13081326