[en] The capacitance matrix method has been used in the TRAC and MELPROG transient, thermal-hydraulic, safety-analysis computer programs to solve the multi-dimensional-vessel matrix equations. A full-matrix solver rather than a more efficient banded-matrix solver was used previously because of nonzero elements lying outside the matrix bandwidth. These outlying nonzero elements result from vessel external and internal pipe flow channels connecting non-adjacent cells in the multidimensional vessel component. The capacitance matrix method provides a more efficient solution algorithm by solving the banded portion of the vessel-matrix equation with a banded-matrix solver. The effect of the nonzero outlying elements on that solution is accounted for through matrix algebra and a lower order capacitance-matrix equation solution that modifies the banded-matrix solution to give the full-matrix solution. 5 refs., 2 figs