Differential algebraic method is an effective technique in computer numerical analysis.It can exactly implement differentiation up to arbitrary high order.The principle of differential algebraic method is applied to calculate curvilinear-axis aberrations with wide beam for magnetic immersion lenses

and the differential algebraic expressions of arbitrary order aberrations are obtained.An illustrative magnetic immersion lens which has an analytic axial field distribution has been studied by using differential algebraic method of curvilinear-axis aberration analysis.All the second order and the third order geometric aberration diagrams are given.