A note on the numerical solution of the one-line model
Both explicit and implicit time-stepping finite difference schemes are well-known techniques for the numerical solution of the one-line model for shoreline change. The former scheme, although fast and simple, is prone to instability. The latter is unconditionally stable, but is slower, significantly more complicated to program, and its accuracy decreases with increasing time step. Here, a technique known as the method of lines is used to solve the one-line model. The advantages of using this method include: (1) unconditionally stable solutions, (2) accuracy that does not depend on a user-specified computation time step, and (3) simple and flexible coding. By using the method of lines procedure described in this paper, one can readily generate an efficient and adaptable one-line numerical model for use in integrated coastal management.
numerical solutions one-line model finite differences method of lines computational efficiency