Due to the extremely large sizes of power grids, IR drop analysis has become a computationally challenging problem both in terms of runtime and memory usage. It has been shown in  that first-order iterative algorithms based on node-by-node and row-by-row traversals of the power grid have both accuracy and runtime advantages over the well-known Random-Walk method. In this paper, we propose second-order iterative algorithms that can significantly reduce the runtime. The new algorithms are extremely fast, and we prove that they guarantee converge to the exact solutions. Experimental results show that our algorithms outperform the Random-Walk algorithm in  and algorithms in . For a 25-million node problem, while the Random-Walk algorithm takes 2 days with maximum error of 6.1 mV, the fastest algorithm in  takes 50 minutes, and our second-order row-based algorithm takes 32 minutes to get an exact solution. Moreover, we can get a solution with maximum error 2 mV in 10 minutes.