• A MACLAURIN’S SERIES METHOD FOR THE SOLUTION OF THE INITIAL VALUE PROBLEMS FOR NTH ORDER LINEAR DIFFERENTIAL EQUATIONS

Abstract

In this paper, a numerical method for solving the linear initial problems for nth order linear differential equation with constant coefficient and analytic initial condition of independent variable is presented. The technique is based upon the Maclaurin’s Theorem. Properties and the initial condition for differential equation is presented. These properties are used to reduce the differential equation to Maclaurin’s theorem of the system. The Maclaurin’s theorem may not converge if the solution is not analytic in whole domain, however, the present method can be applied to initial value problem for linear differential equation, when the solution is analytic in the interior of the domain. The method is computationally very attractive and applications are demonstrated through illustrative examples.