Fig. 1

Schematic diagrams of spatiotemporal discretization for time-marching schemes investigated in the present study. a Cochard and Madariaga (1994) (CM) and b the present scheme (NL). Collocation points where \( V \) and \( \tau \) are defined are indicated by circles, and \( V \) at the points indicated by crosses are stored and used in numerical integration. Piecewise-constant approximation was adopted in both schemes, and a basis function is indicated by a gray square. Thick dashed line in b indicates that the collocation points (circles) are not included in the support of the basis function