An Adaptive Spline Wavelet ADI (SW-ADI) Method for Two-Dimensional Reaction–Diffusion Equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1998 English Publisher:Elsevier BVJournal:Journal of Computational Physics, volume 139, pages 92-126 (issn: 0021-9991,

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Authors: Cai, Wei; Zhang, Wu;

doi: 10.1006/jcph.1997.5865

An Adaptive Spline Wavelet ADI (SW-ADI) Method for Two-Dimensional Reaction–Diffusion Equations

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Abstract

A wavelet-based ADI method for 2D unsteady reaction-diffusion equation is described. Cubic and quintic wavelet approximations to functions and their derivatives with emphasize on boundary wavelets are outlined. A fast wavelet transform, data structure and adaptive procedure are discussed. As a time stepping method, the ADI technique is considered. Numerical results showing nearly second-order accuracy are presented.

Related Organizations

University of North Carolina at Chapel Hill
United States
University of North Carolina at Charlotte
United States

Keywords

numerical examples, reaction-diffusion equations, Reaction-diffusion equations, fast wavelet transform, adaptive spline wavelet method, wavelets, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, alternative directions method, time stepping method

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