{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:53:04Z","timestamp":1747191184291,"version":"3.40.5"},"reference-count":30,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,4,15]],"date-time":"2022-04-15T00:00:00Z","timestamp":1649980800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2022,4,15]]},"abstract":"<jats:p>In this paper, perturbed Galerkin method is proposed to find numerical solution of an integro-differential equations using fourth kind shifted Chebyshev polynomials as basis functions which transform the integro-differential equation into a system of linear equations. The systems of linear equations are then solved to obtain the approximate solution. Examples to justify the effectiveness and accuracy of the method are presented and their numerical results are compared with Galerkin\u2019s method, Taylor\u2019s series method, and Tau\u2019s method which provide validation for the proposed approach. The errors obtained justify the effectiveness and accuracy of the method.<\/jats:p>","DOI":"10.1155\/2022\/9748558","type":"journal-article","created":{"date-parts":[[2022,4,15]],"date-time":"2022-04-15T22:35:09Z","timestamp":1650062109000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Perturbed Galerkin Method for Solving Integro-Differential Equations"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7126-5781","authenticated-orcid":true,"given":"K.","family":"Issa","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8026-2999","authenticated-orcid":true,"given":"J.","family":"Biazar","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Guilan, Rasht, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. 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