New Midpoint-based Approach for the Solution of n-th Order Differential Equations

This paper proposes a new technique to solve n-th order linear uncertain but bounded (interval) differential equations with interval initial conditions using the interval midpoint. First, the interval differential equation is solved in terms of the interval midpoint. This solution is then used to find the solution of the original interval differential equation. The method is discussed by considering various cases for the coefficients in the differential equation with examples. We have compared the results obtained by the proposed method with exact and homotopy perturbation method (HPM) to demonstrate the validity and applicability of the method.