Abstract: A new explicit method for numerical simulation of wave motion in time domainis first presented and illustrated by constructing the recursion formulas atnodal points of an irregular grid for 1-D wave equation in this paper. Todemonstrate the possibility to develop stable and high-order formulas withthe method, accuracy and stability of the numerical simulation are firstdiscussed in detail for the 1-D scalar wave equation in a uniform grid, andan approach is then proposed to construct the stable formulas with 2M-orderaccuracy both in time and space. A theoretical case is illustrated byconstructing the formulas of second order (M=1) and fourth order (M=2). Theresults with the proposed method are validated by a series of numericaltests.