Abstract
In this paper, a new method for the numerical solution of the two-dimensional parabolic equation of Tappert in horizontally-stratified media is presented. This method uses orthogonal cubic spline collocation for the semidiscretization with respect to depth, and the resulting system of differential-algebraic equations is solved using the NAG Library routine D02NNF. In the present application, orthogonal spline collocation, which has been exceedingly effective in the approximate solution of a broad class of problems, has the advantage that it systematically incorporates the requisite interface conditions. The state-of-the-art routine D02NNF, which implements backward differentiation formulas, has been used successfully in the solution of related problems.
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