Finite difference methods for the wide-angle "parabolic" equation

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1998 (EN)
Finite difference methods for the wide-angle "parabolic" equation (EN)

Akrivis, G. (EN)

Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Χημείας (EL)
Akrivis, G. (EN)

We consider a model initial and boundary value problem for the wide-angle "parabolic" equation Lu-r = icu of underwater acoustics, where L is a second-order differential operator in the depth variable z with depth- and range-dependent coefficients. We discretize the problem by the Crank-Nicolson finite difference scheme and also by the forward Euler method using nonuniform partitions both in depth and in range. Assuming that the problem admits a smooth solution, and L is invertible for all r under the posed boundary and interface conditions, we show stability of both schemes and derive error estimates. (EN)

wide-angle parabolic equation (EN)

Πανεπιστήμιο Ιωαννίνων (EL)
University of Ioannina (EN)

Siam Journal on Numerical Analysis (EN)



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