CHEBYSHEV MATRIX METHODS FOR THE HEAT EQUATION: CONVERGENCE AND ACCURACY.
Solutions to the steady state heat equation are obtained using the Chebyshev-Tau matrix method. This technique employs a Chebyshev series representation for the temperature field with unknown coefficients which are selected so that the dynamical equation and boundary conditions are satisfied to a high degree of approximation. Algebraic equations describing the behavior of the Chebyshev coefficients are derived using a matrix formulation which allows easy problem preparation. The accuracy and convergence properties of the Chebyshev expansion are discussed in general, and illustrated for the radial heat conduction pro blem in a homogeneous cylindrical shell. A final section describes some current research on multi-dimensional problems, irregular domains, variable thermal conductivity, heat sources and sinks, and complicated boundary conditions.
