A　Differential　algebraic　method　is　of　an　effective　technique　in　computer　numerical　analysis.　It　implements　conveniently　differentiation　up　to　arbitrary　high　order,　based　on　the　nonstandard　analysis.　In　this　paper,　the　differential　algebra　(DA)　method　has　been　employed　to　compute　the　high　order　aberrations　up　to　the　fifth　order　of　electron　lenses　with　quadrupole　and　octupole　corrector　whose　electric/magnetic　fields　are　in　the　forms　of　discrete　arrays,　for　example,　the　files　computed　by　FEM　or　FDM　method.　The　quadrupole　and　octupole　electro-magnetic　fields　of　arbitrary　point　are　obtained　by　local　analytic　expressions,　and　then　field　potentials　are　transformed　into　new　forms　which　can　be　operated　in　the　DA　calculation.　The　program　has　been　developed　and　tested　as　well.　The　geometric　and　chromatic　aberrations　coefficients　up　to　fifth　order　of　electron　lenses　with　quadrupole　and　octupole　corrector　are　calculated　by　the　developed　program.