in this talk, we study the property of the solution of semidefinite programs with multi-dimensional perturbation variables using the davidenko di erential equations. under the assumptions of strict complementary and non-degeneracy, we aim to find the a priori unknown maximal convex permissible perturbation set where the semidefinite program has a unique optimum and the optimum is analytic. a sweeping euler numerical method is developed to approximate this a priori unknown perturbation set and solve the semidefinite program within this set. we prove local and global error bounds for this second-order sweeping euler scheme and demonstrate results on several examples.