Yıldız G.Tınaztepe G.Sezer M.2024-07-222024-07-22202015261492http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/14251In this article, we approximate the solution of high order linear Fredholm integro-differential equations with a variable coefficient under the initial-boundary conditions by Bell polynomials. Using collocation points and treating the solution as a linear combination of Bell polynomials, the problem is reduced to linear system of equations whose unknown variables are Bell coefficients. The solution to this algebraic system determines the approximate solution. Error estimation of approximate solution is done. Some examples are provided to illustrate the performance of the method. The numerical results are compared with the collocation method based on Legendre polynomials and the other two methods based on Taylor polynomials. It is observed that the method is better than Legendre collocation method and as accurate as the methods involving Taylor polynomials. © 2020 Tech Science Press. All rights reserved.EnglishAll Open Access; Gold Open AccessBellsBoundary conditionsIntegrodifferential equationsLinear systemsNumerical methodsApproximate solutionCollocation pointsFredholm integro-differential equationsLegendre polynomialsLegendre-collocation methodLinear combinationsLinear system of equationsVariable coefficientsPolynomialsArticle10.32604/cmes.2020.09329