{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:25:55Z","timestamp":1760145955132,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T00:00:00Z","timestamp":1726876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The computational study of fixed-point problems in distance spaces is an active and important research area. The purpose of this paper is to construct a new iterative scheme in the setting of Banach space for approximating solutions of fixed-point problems. We first prove the strong convergence of the scheme for a general class of contractions under some appropriate assumptions on the domain and a parameter involved in our scheme. We then study the qualitative aspects of our scheme, such as the stability and order of convergence for the scheme. Some nonlinear problems are then considered and solved numerically by our new iterative scheme. The numerical simulations and graphical visualizations prove the high accuracy and stability of the new fixed-point scheme. Eventually, we solve a 2D nonlinear Volterra Integral Equation (VIE) via the application of our main outcome. Our results improve many related results in fixed-point iteration theory.<\/jats:p>","DOI":"10.3390\/computation12090192","type":"journal-article","created":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T04:45:28Z","timestamp":1727066728000},"page":"192","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational Analysis of a Novel Iterative Scheme with an Application"],"prefix":"10.3390","volume":"12","author":[{"given":"Fayyaz","family":"Ahmad","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6991-4287","authenticated-orcid":false,"given":"Kifayat","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8119-9546","authenticated-orcid":false,"given":"Junaid","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2073","authenticated-orcid":false,"given":"Ahmad","family":"Aloqaily","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney 2150, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s40314-021-01749-3","article-title":"Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems","volume":"41","author":"Alakoya","year":"2022","journal-title":"Comput. 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