The Hyers-Ulam Stability for High-Order Linear Differential Equations with Constant Coefficients

There are many problems in engineering can be reflected by linear ordinary differential equation with constant coefficients. If a differential equation has the Hyers-Ulam stability, then it can guarantee that an approximate solution is close to an accurate solution. So it is important to consider the the Hyers-Ulam stability of differential equations in numerical solution of differential equations. Up to now, the discussion of the Hyers-Ulam stability for high-order differential equations is very few. This paper concerns with the Hyers-Ulam stability of high-order linear differential equations with constant coefficients. We get a necessary and sufficient condition such that a class of differential inequalities hold. Using this necessary and sufficient condition, the formula of general solution and roots of the characteristic equation for linear ordinary differential equation with constant coefficients, we discuss the Hyers-Ulam stability of high-order linear differential equations with constant coefficients. The conclusions show that some third-order and nth-order linear differential equations with constant coefficients have the Hyers-Ulam stability.