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Finite difference methods, when applied to the differential equations modelling energy flows in buildings, give rise to a system of non-linear difference equations. A frequently used direct solution method involving linearization is analysed and a related method proposed. These and one other connected method are compared using a building related test problem prepared for this purpose. The proposed numerical method is found to produce least error, about 30% less than the commonly used method, and it is recommended for inclusion in building energy simulation software. A fundamental method for estimating the pre conditioning period of a building, arising from the work, is discussed.
Crowley, M., Hashmi, S.: Improved direct solver for building energy simulation. Building Services Engineering Research and Technology, Vol. 21, 3, pp.167-173. 2000. doi: 10.1177/014362440002100304