AbstractAn analysis technique that uses the Lanczos vectors to construct a Reyleigh–Ritz solution for the transient heat conduction problem is presented. The Lanczos vectors are derived from the heat supply vector and incorporate all the information peculiar to a given problem. They are orthonormal with respect to the heat capacitance matrix and are generated with a minimum of computational effort. Furthermore, an error bound is derived that can be used to terminate the Lanczos algorithm as soon as the number of vectors required to obtain a desired degree of accuracy has been generated. A summary of the algorithm is presented and the accuracy and efficiency of the method is illustrated using a numerical example.
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