Exponential Euler and Backward Euler Methods for Nonlinear Heat Conduction Problems

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