Adaptive Multiresolution Collocation Methods for Initial Boundary Value Problems of Nonlinear PDEs

We have designed a cubic spline wavelet-like decomposition for the Sobolev space H2 0(I) where I is a bounded interval. Based on a special point value vanishing property of the wavelet basis functions, a fast discrete wavelet transform (DWT) is constructed. This DWT will map discrete samples of a fu...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 33; no. 3; pp. 937 - 970
Main Authors: Cai, Wei, Wang, Jianzhong
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.1996
Subjects:
Aeronautics
Approximation
Boundary conditions
Boundary value problems
Coefficients
Decomposition
Eigenvalues
Error rates
Exact sciences and technology
Interpolation
Mathematical functions
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Sobolev spaces
Textual collocation
Wavelet transforms
Sobolev space
Initial value problem
Discrete transformation
Adaptive method
Multiresolution analysis
Partial differential equation
Wavelet decomposition
Non linear equation
Numerical analysis
Boundary value problem
Wavelet transformation
Linear algebra
Wavelet base
Equation resolution
Collocation method
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:We have designed a cubic spline wavelet-like decomposition for the Sobolev space H2 0(I) where I is a bounded interval. Based on a special point value vanishing property of the wavelet basis functions, a fast discrete wavelet transform (DWT) is constructed. This DWT will map discrete samples of a function to its wavelet expansion coefficients in at most 7N log N operations. Using this transform, we propose a collocation method for the initial boundary value problem of nonlinear partial differential equations (PDEs). Then, we test the efficiency of the DWT and apply the collocation method to solve linear and nonlinear PDEs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0036-1429
1095-7170
DOI:10.1137/0733047