A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Sarra, Scott A. and Musgrave, Derek and Stone, Marcus and Powell, Joseph I. (2024) A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems. Journal of Applied Mathematics and Physics, 12 (07). pp. 2559-2573. ISSN 2327-4352

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Abstract

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

Item Type: Article
Subjects: GO for STM > Mathematical Science
Depositing User: Unnamed user with email support@goforstm.com
Date Deposited: 24 Jul 2024 10:30
Last Modified: 24 Jul 2024 10:30
URI: http://archive.article4submit.com/id/eprint/2946

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