Differential algebraic method is an effective technique in computer numerical analysis.It can exactly implement differentiation up to arbitrary high order based on the nonstandard analysis theory.The principle of differential algebraic method is applied to calculate arbitrary high order aberrations of electrostatic electron lens systems.An example is given to show that the numerical results have excellent accuracy

and the accuracy is limited only by the machine precision and the arithmetic errors.The arbitrary high order aberrations are conveniently calculated by differential algebra method and the fifth-order aberration diagrams are given.