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講者

Collocation and Shape Parameter

Lin-Tian Luh

Abstract

In this talk we are going to present a completely new approach to solving differential equations. Based on the newly born choice theory of the shape parameters, the collocation method can achieve efficiently very high accuracy without constructing meshes. The radial basis functions used are multiquadrics and inverse multiquadrics. The optimal choice of their shape parameters are shown in a concrete way, called the MN curves. Although the construction of this kind of curves is a nontrivial task, their final form is very clear and easy to understand. It means that the crux of making collocation has been solved and our approach is useful.

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