Abstract
A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variable diffusion coefficients. The efficiency of the computational algorithm with respect to the finite analytic coefficients has been improved, while the inherent accuracy and stability of the original method is preserved. Therefore, the algorithm is a valuable tool for diverse engineering applications, governed by the same conduction-type mathematical model: heat conduction, mass diffusion, flow through porous media, fully developed duct flows, lubrication flows, electromagnetic field theory and diffusion models of thermal radiation.
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