Solving a one-dimensional moving boundary problem based on wave digital principles

We report on a novel method for solving one-dimensional moving boundary problems based on wave digital principles. Here, we exploit multidimensional wave digital algorithms to derive an efficient and robust algorithm for the solution of the considered problem. Our method lets the wave digital model, on which the algorithm is based, expand according to the size of the solution domain. The expanding model introduces new dynamical elements, which must be properly initialized to obtain a calculable algorithm. To deal with this problem, we make use of linear multistep methods to extrapolate the missing values. Our results show the proposed method to indeed be capable of correctly solving a one-dimensional partial differential equation describing a growing biological axon.