A fast adaptive spectral graph wavelet method for the viscous Burgers' equation on a star‐shaped connected graph. (12th December 2019)

• Record Type: Journal Article
• Authors: Shukla, Ankita; Mehra, Mani; Leugering, Günter
• Other Names: Simos Theodore guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 13(2020)
• Page Start: 7595
• Page End: 7614
• Publication Date: 2019-12-12
• Subjects: adaptive node arrangement -- Burgers' equation -- connected graph -- spectral graph wavelet; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5907
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Water wave propagation in an open channel network can be described by the viscous Burgers' equation on the corresponding connected graph, possibly with small viscosity. In this paper, we propose a fast adaptive spectral graph wavelet method for the numerical solution of the viscous Burgers' equation on a star‐shaped connected graph. The vital feature of spectral graph wavelets is that they can be constructed on any complex network using the graph Laplacian. The essence of the method is that the same operator can be used for the construction of the spectral graph wavelet and the approximation of the differential operator involved in the Burgers' equation. In this paper, two test problems are considered with homogeneous Dirichlet boundary condition. The numerical results show that the method accurately captures the evolution of the localized patterns at all the scales, and the adaptive node arrangement is accordingly obtained. The convergence of the given method is verified, and efficiency is shown using CPU time.