论文标题
非线性热传导问题的指数欧拉和向后欧拉方法
Exponential Euler and backward Euler methods for nonlinear heat conduction problems
论文作者
论文摘要
在本文中，提出了一种非线性指数EULER方案的变体来解决非线性热传导问题。该方法基于非线性迭代，在每次迭代中，必须解决线性初始值问题。我们将此方法与向后的Euler方法与非线性迭代相结合。对于这两种方法，我们都显示了解决方案的单调性和界限，并提供了足够的条件，以使非线性迭代收敛。提出了数值测试以检查两个方案的性能。提出的指数Euler方案是基于重新启动的Krylov子空间方法实施的，因此实际上是明确的（仅涉及矩阵向量产品）。
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).
