An improved implementation of generalized Adams methods for underwater wave propagation problems (Q1058933)

As previously demonstrated [the first and the third author, ibid. 7, 195- 202 (1980; Zbl 0451.76074)] the generalized Adams method (GAM) is effective for solving underwater acoustic wave-propagation problems. In this paper, we describe how to modify an earlier GAM implementation to substantially improve its efficiency. An approximation to the matrix exponential is required to implement a GAM. By using a rational approximation implicitly, the sparsity of the matrix can be exploited to produce a significantly more efficient implementation for a wide class of problems. A further improvement in efficiency can be gained by using a restricted-Padé approximation to the matrix exponential, rather than the more traditional Padé approximation. To demonstrate the effectiveness of this approach, an unerwater acoustic wave-propagation problem in a wedge-shaped region is solved by both the modified and unmodified GAM implementations.