Waveguide　discontinuity　problems　are　treated　as　three　substructures　which　are　homogeneous　in　the　longitudinal　direction.　Transverse　section　is　discretized　by　edge　element.　The　export　stiff　matrices　can　be　calculated　by　the　precision　integration　based　on　Riccati　equations　in　Hamilton　system.　The　whole　waveguide　discontinuity　problems　can　be　solved　by　a　combination　of　substructures.　This　method　can　deduce　the　dimension　of　the　equations　only　because　of　transverse　discretization.　The　calculation　is　independent　of　the　increment　of　the　longitudinal　length　because　of　precise　integration.　Thus　the　longitudinal　length　can　be　long　enough　to　assure　precision.