Amoozad, TaherAllahviranloo, TofighAbbasbandy, SaeidMalkhalifeh, Mohsen Rostamy2024-05-192024-05-1920240031-89491402-4896https://doi.org10.1088/1402-4896/ad1eabhttps://hdl.handle.net/20.500.12713/5538This article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.eninfo:eu-repo/semantics/closedAccessReproducing Kernel MethodLinear Volterra Integral EquationsConvergence AnalysisError AnalysisArticle992WOS:0011486985000012-s2.0-85183914029N/A10.1088/1402-4896/ad1eabQ2