# CHEBYSHEV MATRIX METHODS FOR THE HEAT EQUATION: CONVERGENCE AND ACCURACY.

Journal Article

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.

### Duke Authors

### Cited Authors

- Shaughnessy, EJ; McMurray, JT

### Published Date

- 1979

### Published In

- ASME Pap