{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:35:22Z","timestamp":1760060122597,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study introduces two novel methodologies for solving systems of Fredholm integral equations, with particular emphasis on second-kind equations. The first method integrates the Sinc-collocation technique with a newly developed singular exponential transformation, enhancing convergence behavior and numerical stability. A comprehensive convergence analysis is conducted to support this approach. The second method employs a double exponential transformation, leading to a pair of linear equations whose solvability is established using the double projection method. Rigorous theoretical analysis is presented, including convergence theorems and newly derived error bounds. A system of two Fredholm integral equations is treated as a practical case study. Numerical examples are provided to illustrate the effectiveness and accuracy of the proposed methods, substantiating the theoretical results.<\/jats:p>","DOI":"10.3390\/axioms14080596","type":"journal-article","created":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T08:46:55Z","timestamp":1754383615000},"page":"596","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New Applications and Improvements of Sinc Functions for Solving a System of Fredholm Integral Equations"],"prefix":"10.3390","volume":"14","author":[{"given":"Saeed","family":"Althubiti","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0791-5866","authenticated-orcid":false,"given":"Abdelaziz","family":"Mennouni","sequence":"additional","affiliation":[{"name":"Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boula\u00efd, Fesdis, Batna 05078, Algeria"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1016\/j.cnsns.2009.04.021","article-title":"Sinc-numerical solution for the Volterra integro-differential equation","volume":"15","author":"Zarebnia","year":"2010","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/S0377-0427(00)00348-4","article-title":"Summary of Sinc-numerical methods","volume":"121","author":"Stenger","year":"2000","journal-title":"J. Comput. Appl. Math."},{"key":"ref_3","first-page":"806","article-title":"Numerical solution of linear integral equations by using Sinc-collocation method","volume":"168","author":"Rashidinia","year":"2005","journal-title":"Appl. Math. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10543-010-0289-x","article-title":"Improvement of a Sinc-collocation method for Fredholm integral equations of the second kind","volume":"51","author":"Okayama","year":"2011","journal-title":"BIT Numer. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"897","DOI":"10.2977\/prims\/1145474600","article-title":"Discovery of the Double Exponential Transformation and Its Developments","volume":"41","author":"Masatake","year":"2005","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.cam.2004.09.019","article-title":"Numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation","volume":"177","author":"Muhammad","year":"2005","journal-title":"J. Comput. Appl. Math."},{"key":"ref_7","first-page":"125693","article-title":"Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the Sinc-collocation method based on the double exponential transformation","volume":"392","author":"Qiu","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.apnum.2020.09.011","article-title":"The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel","volume":"159","author":"Qiu","year":"2021","journal-title":"Appl. Numer. Math."},{"doi-asserted-by":"crossref","unstructured":"Lund, J., and Bowers, K.L. (1992). Sinc-Methods for Quadrature and Differential Equations, SIAM.","key":"ref_9","DOI":"10.1137\/1.9781611971637"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3292","DOI":"10.1016\/j.camwa.2011.08.045","article-title":"Application of Sinc-collocation method for solving a class of nonlinear Fredholm integral equations","volume":"62","author":"Maleknejad","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.cam.2007.06.014","article-title":"Numerical treatment of second kind Fredholm integral equations systems on bounded intervals","volume":"217","author":"Laurita","year":"2008","journal-title":"J. Comput. Appl. Math."},{"key":"ref_12","first-page":"126173","article-title":"Approximation methods for system of linear Fredholm integral equations of second kind","volume":"403","author":"Chakraborty","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.cam.2003.05.002","article-title":"Double exponential formulas for numerical indefinite integration","volume":"161","author":"Muhammad","year":"2003","journal-title":"J. Comput. Appl. Math."},{"unstructured":"Ahues, M., Largillier, A., and Limaye, B.V. (2011). Spectral Computations for Bounded Operators, Chapman and Hall\/CRC.","key":"ref_14"},{"key":"ref_15","first-page":"63","article-title":"A new efficient strategy for solving the system of Cauchy integral equations via two projection methods","volume":"14","author":"Mennouni","year":"2022","journal-title":"Transylv. J. Math. Mech."},{"doi-asserted-by":"crossref","unstructured":"Kress, R. (1998). Numerical Analysis, Springer.","key":"ref_16","DOI":"10.1007\/978-1-4612-0599-9"},{"key":"ref_17","first-page":"297","article-title":"Solving Fredholm integral equations using with Chebyshev polynomials","volume":"2","author":"Danaei","year":"2015","journal-title":"Int. J. Innovative Sci. Eng. Technol."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/596\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:20:54Z","timestamp":1760034054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/596"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,1]]},"references-count":17,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["axioms14080596"],"URL":"https:\/\/doi.org\/10.3390\/axioms14080596","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,8,1]]}}}