Block-marching in time with DQ discretization: an efficient method for time-dependent problems

Abstract In this paper, an efficient method is presented to solve time-dependent problems. The proposed method marches in the time direction block by block. In each block, there are several time levels, and the numerical results at these time levels are obtained simultaneously. The global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives. The proposed method is validated by a sample problem, which has an exact solution for easy comparison. It was found that as compared to the conventional 4-stage Runge–Kutta method, the present method could give much higher order of accuracy for numerical results and require much less computational effort.