The　waveguide　is　decomposed　into　several　substructures　in　the　longitudinal　direction,　and　PML　absorbing　boundary　is　treated　as　one　of　them.　The　transverse　section　of　the　substructures　is　discretized　with　the　finite　element　method,　a　precise　integration　method　based　on　the　Riccati　equations　is　used　for　the　longitudinal　integration　to　generate　the　export　stiffness　matrices,　and　then　the　waveguide　discontinuity　problems　are　expected　to　be　solved　through　the　combination　of　the　substructures.　Numerical　examples　demonstrate　that,　the　waveguide　discontinuity　problems　can　be　effectively　solved　with　this　method,　the　disadvantage　that　the　artificial　boundary　must　be　far　away　from　the　non-uniform　region　can　be　overcome,　and　the　field　near　the　non-uniform　region　can　be　worked　out.