The Letter studies the problem of numerical approximations of the critical transition temperature and the energy gap function in the Bardeen-Cooper-Schrieffer equation arising in superconductivity theory. The positive kernel function leads to a phonon-dominant state at zero temperature. Much attention is paid to the equation defined on a bounded region. Two discretized versions of the equation are introduced. The first version approximates the desired solution from below, while the second, from above. Numerical examples are presented to illustrate the efficiency of the method. Besides, the approximations of a full space solution and the associated critical temperature by solution sequences constructed on bounded domains are also investigated.
- Mathematics Subject Classifications (1991): 82B26, 83D55, 45G10, 45L
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics