In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, orthogonal polynomials, namely, shifted fifth-kind Chebyshev polynomials (5CPs), are used. The proposed method’s derivation based on solving integral that corresponds original problem. approach and some theoretical findings serve transform problem with its underlying conditions into suitabl...

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In this paper we describe the use of multivariate Chebyshev polynomials in computing spectral derivations and Clenshaw–Curtis type quadratures. The multivariate Chebyshev polynomials give a spectrally accurate approximation of smooth multivariate functions. In particular we investigate polynomials derived from the A2 root system. We provide analytic formulas for the gradient and integral of A2 ...