Numerical solution of the three-dimensional analogue of Goursat's problem

✍ Scribed by I.E. Mikhailov

• Publisher: Elsevier Science
• Year: 1983
• Weight: 327 KB
• Volume: 23
• Category: Article
• ISSN: 0041-5553
• DOI: 10.1016/s0041-5553(83)80171-2

✦ Synopsis

on the shape of the super-cavity /1, 11, 12/; it is illustrated in Fig. 3 by comparing two cavities behind different bodies (A-l and 2) with the same a ; the broken curves show the part of the object inside the cavity. Naturally, with such a small difference of a~/ol from a constant, the values of Band L are virtually indistinguishable from those given by the exact theory /4, 5, 7/.

6. Returning to a discussion of the actual method, it must be mentioned that its convergence depends, as is usually the case in a non-linear problem, on the choice of initialapproximation. Of course the result is influenced by the form of /(x, P) ; and the computation becomes much more complicated with a different order of variation with respect to different variables of the target function and of the components of the normal to the constraints. In certain cases, W had to be maximized with respect to Ph P, and P" P, separately, since the second pair of parameters had a much weaker influence on grad II>.

The approach described represents a reasonable compromise between the demands of accuracy and simplicity when solving non-linear boundary value problems.

The authors thank N.N. Moiseev for useful discussions.