Wavelet-Galerkin method for the Kolmogorov equation
type: Item
instance of: scholarly article
title: Wavelet-Galerkin method for the Kolmogorov equation
zbMATH Open document ID: 1070.65095
published in: Mathematical and Computer Modelling
publication date: 2005-05-12T00:00:00Z
review text: It is well understood that wavelet functions, especially Daubechies' wavelets [cf. \textit{I. Daubechies}, Commun. Pure Appl. Math. 41, 909--996 (1988; Zbl 0644.42026)] provide a powerful tool that can be applied in the finite element method. Using Daubechies' wavelets as basis functions, the authors solve here Kolmogorov equation by a wavelet-Galerkin method. The process consists in deriving a method called the time dependent boundary wavelet Galerkin method. With this method, an initial interval, for the initial-boundary value problem based upon the initial condition of the Kolmogorov equation is determined. Based upon the numerical solution of the initial-boundary value problem, this interval is adjusted during computation. An example is also provided by using Daubechies D4 scaling functions.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 2167465
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: Kolmogorov equation
zbMATH Keywords: wavelet Galerkin method
zbMATH Keywords: Daubechies' wavelets
zbMATH Keywords: numerical example
zbMATH Keywords: Daubechies scaling function
zbMATH Keywords: pyramid algorithm
zbMATH Keywords: finite element method
zbMATH Keywords: initial-boundary value problem
author: Zhi-Gang Liang
author: Stephen Yau
MaRDI profile type: Publication
full work available at URL: j.mcm.2003.07.016
OpenAlex ID: W2049825215
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DOI: 10.1016/J.MCM.2003.07.016
description: scientific article; zbMATH DE number 2167465