中文摘要：

考虑求解一类非线性反应扩散对流方程的块单调迭代算法，其中包括传统的块Picard，块Jacobi，以及在区域分解算法中常用的并行Schwarz算法．所讨论的算法可从问题的一个上解和下解出发，产生一个上解迭代序列和下解迭代序列并单调收敛于离散问题的解．这类算法的优点在于算法的并行结构好且可直接通过所产生的上解和下解迭代序列，得到迭代解的最大模误差界．在理论上，得到了算法的单调收敛性、线陛与超线性收敛性．

英文摘要：

Some parallel block iterative algorithms are presented for solving a discrete system of nonlinear reaction-diffusion-convection equation. The algorithms include traditional block Picard, block Jacobi as well as parallel Schwarz algorithm. It is proved that the algorithms can produce monotone sequences, which converge to the solution of the problem monotonically, from a pair of upper and lower solutions of the problem. The algorithms have a good parallel structure and the monotone property of the algorithms gives improved upper and lower bounds of the solution in each iteration. The convergent rate is estimated for the algorithms. Moreover, the supper-linear or quadratic convergence rate can be proved for the inexact algorithm.