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Numerical evaluation of eigenvalues in notch problems using a region searching method

✍ Scribed by Chen, Y. Z. ;Lin, X. Y. ;Wang, Z. X.

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
110 KB
Volume
22
Category
Article
ISSN
1069-8299

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✦ Synopsis

This paper presents a method for finding the eigenvalues of some equations, or the zeros of analytic functions. There are two steps in the method. In the first step, integration along the edges of rectangle for an analytic function is performed. From the result of integration, one can know whether the zero exists in the rectangle or not. If the zero of an analytic function exists in the rectangle, we can perform the second step. In the second step, the zero is obtained by iteration. Therefore, the method is called a region searching method. Particular advantage of the suggested method is that the process for finding zero can be visualized. For example, one can clearly indicate the rectangles, which contain the zeros of an analytic function. Three numerical examples are presented. The obtained results are satisfactory even for a complicated case, for example, for finding eigenvalues of a composed wedge of dissimilar materials.

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Novel numerical solution technique for evaluating eigenvalues in a plane notch problem
✍ Chen, Y. Z. 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 123 KB 👁 2 views

A novel numerical solution technique for evaluating eigenvalues in a plane notch problem is suggested. In both real value and complex value cases, the problem for evaluating the eigenvalue is reduced to ®nding the roots of a function F(x) 0, and the roots can be evaluated by the well known half-divi