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Partial differential equations play a imperative position in lots of branches of technology and engineering. for this reason it is very important clear up difficulties related to them. One element of fixing a partial differential equation challenge is to teach that it really is well-posed, i. e. , that it has one and just one answer, and that the answer relies constantly at the facts of the matter. one other element is to procure targeted quantitative information regarding the answer. the normal procedure for doing this was once to discover a illustration of the answer as a chain or fundamental of identified precise features, after which to judge the sequence or necessary through numerical or via asymptotic tools. the inability of this system is that there are particularly few difficulties for which such representations are available. as a result, the conventional strategy has been changed through equipment for direct answer of difficulties both numerically or asymptotically. this text is dedicated to a selected procedure, referred to as the "ray method," for the asymptotic resolution of difficulties for linear partial differential equations governing wave propagation. those equations contain a parameter, akin to the wavelength. . \, that is small in comparison to all different lengths within the challenge. The ray approach is used to build an asymptotic enlargement of the answer that's legitimate close to . . \ = zero, or equivalently for ok = 21r I A close to infinity.
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