A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations

In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for deri...

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Bibliographic Details
Published in:Mathematical and computer modelling 2011-12, Vol.54 (11), p.2858-2868
Main Authors: Shi, Zhi, Cao, Yong-yan
Format: Article
Language:English
Subjects:
Biharmonic equation
Exact sciences and technology
Fourier analysis
Haar wavelet
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Poisson equation
Sciences and techniques of general use
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Summary:In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obtained system of algebraic equations. The efficiency of the method is demonstrated by four numerical examples.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.07.006