A nonlinear boundary value problem for the steady-state one-dimensional heat conduction equation

The numerical solution is discussed of a two-point boundary value problem, arising in RF superconductivity, for the steady-state one-dimensional heat conduction equation with thermal conductivity depending on temperature and boundary conditions nonlinearly involving temperature and heat flux. The numerical method employed attains a great computational saving in comparison with standard ones by tacking advantage of the particular features of our problem and can be likewise applied to other problems. The general mathematical form a problem must have for being solved by the aforementioned method is then laid down