【摘要】 本文构造了求解刚性常微分方程的并行广义Rosenbrock方法 (PEROWs) ,分析了方法的收敛性和数值稳定性 .通过用Powell方法优化方法的稳定域 ,构造了二级四阶并行格式PEROW4 ,并证明该方法是A 稳定的 .新方法比同级的并行Rosenbrock方法MPROW3及PRM3均高一阶 ,因而在计算精度上处于优势 .此外 ,PEROW4能使得各处理机上的负载基本均衡 ,从而达到非常理想的加速比和并行效率 .更多还原

【Abstract】 In this paper parallel extended Rosenbrock methods for solving stiff ordinary differential equations is constructed. Convergence and stability of these methods are discussed. The formula of two-stage fourth-order is obtained by choosing free parameters appropriately, and is proved it is A-stable. The convergence order of the method has one more than that of parallel Rosenbrock methods of the same stage, so it stands obviously in an advantage position in the computational accuracy. Moreover, the computation workload assigned to each processor is roughly balanced, so the method of two-stage fourth-order can obtained ideal speed-up and parallel efficiency.更多还原