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The Generalized Integral Representation Method (GIRM) forSpace-Time-Separated Method (STSM) and Space-Time-Unified Method (STUM) arediscussed. STSM and STUM give explicit and implicit time evolutions,respectively. The algorithm of STSM is much simpler than STUM. However, theimplicit time evolution of STUM could give us much more efficient computation.Numerical calculations using STUM for Dirichlet and Neumann problems in 2Dspace-time are conducted using a Traditional Fundamental Solution (TFS). Theresults seem very satisfactory. However, in case of Neumann problem, the timeincrement must be smaller than in case of Dirichlet problem.

Space-time-unified GIRM (Generalized Integral Representation Method) for unsteady advective diffusion