Premium
Solutions of boundary‐value problems by the Lanczos–Chebyshev reduction method
Author(s) -
Chen Peter Y. P.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170212
Subject(s) - lanczos resampling , mathematics , boundary value problem , thermal conduction , chebyshev equation , mathematical analysis , chebyshev polynomials , partial differential equation , eigenvalues and eigenvectors , reduction (mathematics) , cylinder , chebyshev filter , chebyshev iteration , rotational symmetry , geometry , physics , orthogonal polynomials , thermodynamics , classical orthogonal polynomials , quantum mechanics
The reduction of liner partial differential equations for boundary‐value problems to ordinary differential equations by the Lanczos‐Chebyshev method is discussed and illustrated by applications to linear stress analysis and heat conduction in axisymmetric cylinders. Numerical examples given include eigenvalues for self‐equilibrating end load problems in hollow cylinders, and heat conduction in a semi‐infinite cylinder. Heat conduction in an infinite half‐space is treated by considering a large multi‐annular cylinder. The simplicity of the Lanczos‐Chebyshev reduction method and its speed and accuracy are demonstrated.