| Summary: | In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials (<i>5CPs</i>), are used. The proposed method’s derivation is based on solving the integral equation that corresponds to the original problem. The tau approach and some theoretical findings serve to transform the problem with its underlying conditions into a suitable system of equations that can be successfully solved by the Gaussian elimination method. For the applicability and precision of our suggested algorithm, some numerical examples are given.
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