A　novel　numerical　method,　referred　to　as　the　Riccati　precise-integration　time-domain　(Riccati-PITD)　method,　is　proposed　to　reduce　the　memory　requirement　of　the　conventional　PITD　method.　In　the　Riccati-PITD　method,　the　electromagnetic　field　components　of　the　transverse　electric/transverse　magnetic　(TE/TM)　wave　are　arranged　in　a　matrix　for　constructing　the　Riccati　matrix　differential　equations　(RDEs)　about　Maxwell＇s　curl　equations.　Then　the　precise　integration　technique　is　adopted　for　the　numerical　integration　of　the　RDEs.　Theoretical　analyses　about　the　memory　requirements　of　the　conventional　and　the　Riccati-PITD　methods　are　presented.　It　is　found　that　the　memory　requirement　can　be　more　greatly　reduced　by　solving　the　electromagnetic-field　components　in　the　form　of　the　matrices　in　the　Riccati-PITD　method　rather　than　in　the　form　of　the　vectors　in　the　conventional　PITD　method.　Numerical　examples　are　also　given　to　confirm　that　the　proposed　method　has　significant　advantages　over　the　conventional　PITD　method　with　respect　to　the　execution　time　and　the　memory　requirement.