A finite-difference solution to a mixed-type partial differential equation: An ocean dynamic motion model (Q1100040)

A mixed-type (hyperbolic, parabolic, elliptic) partial differential equation, which results from a model of a towed cylindrical acoustic antenna in the ocean, has been solved by combining the techniques of the method of lines and the numerical ordinary differential equation method. The model describes the transverse dynamic motion of a zero bending rigidity cylinder in an axial viscous stream. This initially ill-posed problem was satisfactorily solved by the above approach. The efficiency of this numerical solution has been improved over previous solutions. Discussions of these improvements are the main theme of this paper which presents an explicit finite-difference scheme; the improvements increase computation speed while maintaining the required accuracy. The improvements are discussed both theoretically and computationally with respect to consistency, stability and convergence. The results of a numerical test example are given.