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Coupled problems result in very stiff problems whose characteristic parameters differ with several orders in magni-tude. For such complex problems, solving them monolith-ically becomes prohibitive. Since nowadays there are optimized solvers for particular problems, solving uncoupled problems becomes easy since each can be solved indepen-dently with its dedicated optimized tools. Therefore the co-simulation of the sub-problems solvers is encouraged. The design of the transmission coupling conditions between solvers plays a fundamental role. The current paper applies the waveform relaxation methods for co-simulation of the finite element and circuit solvers, investigate the contribu-tion of higher order integration methods and also consid-ers the the theoretical modelling of a boost converter. The method is illustrated on a coupled finite element inductor and a boost converter and focuses on the comparison of the transmission coupling conditions based on the waveform iteration numbers between the two sub-solvers. We demonstrate that for lightly coupled systems the dynamic itera-tions between the sub-solvers depends much on the inter-nal integrators in individual sub-solvers whereas for tightly coupled systems it depends also to the kind of transmission coupling conditions., SCOPUS: ar.j, info:eu-repo/semantics/published