Durmaz, Muhammet EnesAmirali, IlhameAmiraliyev, Gabil M.2023-07-262023-07-2620231598-58651865-2085https://doi.org/10.1007/s12190-022-01757-4https://hdl.handle.net/20.500.12684/12951In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.en10.1007/s12190-022-01757-4info:eu-repo/semantics/openAccessFinite Difference Scheme; Fredholm Integro-Differential Equation; Integral Boundary Condition; Shishkin Mesh; Singular Perturbation; Uniform ConvergenceArticle691505528356985732-s2.0-85131585126WOS:000808410800001Q2Q1