On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations
In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra−Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also pr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/10/1200 |
| _version_ | 1811305723598995456 |
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| author | Sanda Micula |
| author_facet | Sanda Micula |
| author_sort | Sanda Micula |
| collection | DOAJ |
| description | In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra−Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed. |
| first_indexed | 2024-04-13T08:31:35Z |
| format | Article |
| id | doaj.art-c6355af35ab7405bb3e17e5a123587e7 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:31:35Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c6355af35ab7405bb3e17e5a123587e72022-12-22T02:54:15ZengMDPI AGSymmetry2073-89942019-09-011110120010.3390/sym11101200sym11101200On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral EquationsSanda Micula0Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaIn this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra−Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed.https://www.mdpi.com/2073-8994/11/10/1200mixed Volterra–Fredholm integral equationsfixed-point theoryPicard iterationnumerical approximationcubature formulas |
| spellingShingle | Sanda Micula On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations Symmetry mixed Volterra–Fredholm integral equations fixed-point theory Picard iteration numerical approximation cubature formulas |
| title | On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations |
| title_full | On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations |
| title_fullStr | On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations |
| title_full_unstemmed | On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations |
| title_short | On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations |
| title_sort | on some iterative numerical methods for mixed volterra fredholm integral equations |
| topic | mixed Volterra–Fredholm integral equations fixed-point theory Picard iteration numerical approximation cubature formulas |
| url | https://www.mdpi.com/2073-8994/11/10/1200 |
| work_keys_str_mv | AT sandamicula onsomeiterativenumericalmethodsformixedvolterrafredholmintegralequations |