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A. Takayuki, “Interpolated Differential Operator (IDO) Scheme for Solving Partial Differential Equations,” Computer Physics Communications, Vol. 102, No. 1-3, 1997, pp. 132-146.

has been cited by the following article:

• TITLE: Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method

  AUTHORS: Hossam S. Hassan, Khaled T. Ramadan, Sarwat N. Hanna

  KEYWORDS: Shallow Water Equations, Fractional Steps Method, Riemann Invariants, Bottom Topography, Cubic Spline Interpolation

  JOURNAL NAME: Applied Mathematics, Vol.1 No.2, July 22, 2010

  ABSTRACT: The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting the multi-dimensional matrix inversion problem into an equivalent one dimensional problem which is successively integrated in every direction along the characteristics using the Riemann invariant associated with the cubic spline interpolation. The height and the velocity field of the shallow water equations over irregular bottom are discretized on a fixed Eulerian grid and time-stepped using the fractional steps method. Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and the free surface elevation have been studied and the results are plotted.