High accurate finite differences based on RBF interpolation and its application in solving differential equations
type: Item
instance of: scholarly article
title: High accurate finite differences based on RBF interpolation and its application in solving differential equations
zbMATH Open document ID: 1410.65416
author: Renzhong Feng
author: Junna Duan
published in: Journal of Scientific Computing
publication date: 2018-09-28T00:00:00Z
review text: The aim of the paper is to develop highly accurate finite difference (FD) approximations to solve differential equations. The tool to be used is the radial basis function (RBF) interpolation with zero degree precision. The Lagrange form of the RBF interpolation is used to avoid the problem of matrix inversion that would arise otherwise. The authors focus on the analysis of truncation errors of two RBF-FD schemes and apply these schemes to three different kinds of differential equations. There is some care needed (and discussed) in how the differential equations are applied to estimate the parameter \(\epsilon\) of the method. The authors conclude with some numerical examples and an implementation discussion.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 6945495
zbMATH Keywords: radial basis function
zbMATH Keywords: RBF
zbMATH Keywords: interpolation
zbMATH Keywords: Lagrange form
zbMATH Keywords: approximation error
zbMATH Keywords: truncation error
reviewed by: Neville J. Ford
MaRDI profile type: Publication
full work available at URL: s10915-018-0684-z
OpenAlex ID: W2790790201
cites work: Q4110059
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DOI: 10.1007/S10915-018-0684-Z
description: scientific article; zbMATH DE number 6945495