Sorkun H.H.Yalçinbaş S.2024-07-222024-07-2220100307904Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18335In this paper, a new approximate method has been presented to solve the linear Volterra integral equation systems (VIEs). This method transforms the integral system into the matrix equation with the help of Taylor series. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Also, this method gives the analytic solution when the exact solutions are polynomials. So as to show this capability and robustness, some systems of VIEs are solved by the presented method in order to obtain their approximate solutions. © 2010.EnglishAll Open Access; Hybrid Gold Open AccessApproximation theoryPolynomialsTaylor seriesAnalytic solutionApproximate methodsApproximate solutionExact solutionIntegral SystemsLinear Volterra integral equationMatrix equationsNew systemSystem of integral equationsSystem of linear algebraic equationsTaylor coefficientsTaylor polynomialsVariable coefficientsVolterra integral equationsIntegral equationsArticle10.1016/j.apm.2010.02.034