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In this paper we consider the conservative averaging method (CAM) for solving the diffusionconvection initial -boundary value problem (IBVP) with piece-wise coefficients in two layered domains. The created special exponential and hyperbolic type approximation functions – splines interpolate the middle integral values of the piece-wise smooth function, and thus the studied IBVP is reduced to the problem of the system of ordinary differential equations. The solution of the corresponding 1-D IBVP with diffusion was obtained also numerically, using the Matlab routine “pdepe” and the numerical solution was compared with the analytical solution. The 1-D diffusion-convection and 1-D diffusion boundary problems were solved and the solutions obtained were analysed with CAM (in case of exponential and hyperbolic splines) and also with Matlab “pdedpe” programme. Higher accuracy of the calculations in solving the 1-D diffusion-convection IBVP (case of discontinuous coefficients with a “jump-off” effect of the solution of IBVP) was identified by CAM. A practical task was solved: the temperature was calculated through the two layered material of gypsum products exposed to fire and the calculations were compared with the results obtained at the Faculty of Environment and Civil Engineering of the Latvia University of Life Sciences and Technologies. The data processing and analysis tools MS Excel and IBM SPSS Statistics20 tested the coincidence of the numerical calculations performed with the above mentioned experimental results.

CAM with special splines for solving of diffusion-convection problems with discontinuous coefficients for layered materials exposed to fire