Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation

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 suitable system of equations can be successfully solved by Gaussian elimination method. For applicability precision our suggested algorithm, numerical examples given.