Kürkçü, Ömür Kıvanç2022-11-282022-11-2820230168-9274https://doi.org/10.1016/j.apnum.2022.10.001https://doi.org/10.1016/j.apnum.2022.10.001https://hdl.handle.net/20.500.13091/3235This study aims to bring together the ultimate formation of the integro-differential equations involving the functional delay and the singular integral with constant delay on the real line, presenting an exclusive spectral computational approach made up of quadratic orthoexponential polynomials. Frankly, the method makes possible to evaluate the singular and delayed integral part by way of the matrix expansion of quadratic property of orthoexponential polynomials, as well as transforming the unknown terms into the matrix relations. Hence, the stability of the integral part is materialized. An error improvement technique is also performed via a residual function. Several integral and integro-differential equations are considered by a devised programme, which immediately returns the method of solution. The outcomes are, thus, exposed to be compared sensitively in tables and figures. Having investigated the comparisons, one can admit that the method accomplishes exclusive and efficient approximation to the equations in question. © 2022 IMACSeninfo:eu-repo/semantics/closedAccessError improvementFunctional delayOrthoexponential polynomialsReal lineSingular integralComputational methodsIntegrodifferential equationsComputational approachConstant delaysDifferential equations with delaysError improvementFunctional delaysIntegral partmatrixOrthoexponential polynomialReal lineSingular integralPolynomialsArticle10.1016/j.apnum.2022.10.0012-s2.0-85140038651