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

Publication ,  Conference
Shaughnessy, EJ; McMurray, JT
Published in: ASME Pap
January 1, 1979

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 Scholars

Published In

ASME Pap

ISSN

0402-1215

Publication Date

January 1, 1979

Issue

79 -HT-62
 

Citation

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Shaughnessy, E. J., & McMurray, J. T. (1979). CHEBYSHEV MATRIX METHODS FOR THE HEAT EQUATION: CONVERGENCE AND ACCURACY. In ASME Pap.
Shaughnessy, E. J., and J. T. McMurray. “CHEBYSHEV MATRIX METHODS FOR THE HEAT EQUATION: CONVERGENCE AND ACCURACY.” In ASME Pap, 1979.
Shaughnessy EJ, McMurray JT. CHEBYSHEV MATRIX METHODS FOR THE HEAT EQUATION: CONVERGENCE AND ACCURACY. In: ASME Pap. 1979.
Shaughnessy, E. J., and J. T. McMurray. “CHEBYSHEV MATRIX METHODS FOR THE HEAT EQUATION: CONVERGENCE AND ACCURACY.ASME Pap, no. 79-HT-62, 1979.

Published In

ASME Pap

ISSN

0402-1215

Publication Date

January 1, 1979

Issue

79 -HT-62