Time varying radial basis functions

0Citations
Citations of this article
10Readers
Mendeley users who have this article in their library.

Abstract

We introduce radial basis functions (RBFs) whose time-varying coefficients determine not only the amplitude and position of each RBF but also their shape. The intended use of these Time Varying-RBFs (TV-RBFs) is in the local-in-time representation of low-dimensional approximations of functions that arise in solving spatiotemporal evolution problems; in particular, for time-varying spatially localized solutions with a temporal translation component such as traveling waves, modulated pulses or soliton-like solutions of evolutionary differential equations. This paper is restricted to the one-dimensional spatial case. We also present an algorithm that places the Time Varying-RBFs (TV-RBFs) over spatiotemporal data that may come from experiments, from finely discretized PDE simulations, or even from multiscale, particle-based simulations. It first approximates the function at a single time instant (a temporal snapshot) as a sum of RBFs using a novel weighted minimization that causes each RBF to primarily approximate one of the localized parts of the function). It then extends that approximation to TV-RBFs over a sequence of snapshots of the function at different times. We conclude by discussing the potential uses of these TV-RBFs.© 2014 Elsevier B.V. All rights reserved.

Author supplied keywords

Cite

CITATION STYLE

APA

Jamshidi, A. A., Gear, C. W., & Kevrekidis, I. G. (2014). Time varying radial basis functions. Journal of Computational and Applied Mathematics, 266, 61–72. https://doi.org/10.1016/j.cam.2014.01.018

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free