  In this paper a variant of nonlinear exponential Euler scheme is proposed for
solving nonlinear heat conduction problems. The method is based on nonlinear
iterations where at each iteration a linear initial-value problem has to be
solved. We compare this method to the backward Euler method combined with
nonlinear iterations. For both methods we show monotonicity and boundedness of
the solutions and give sufficient conditions for convergence of the nonlinear
iterations. Numerical tests are presented to examine performance of the two
schemes. The presented exponential Euler scheme is implemented based on
restarted Krylov subspace methods and, hence, is essentially explicit (involves
only matrix-vector products).
