Adaptive Wavelet Collocation Methods for Initial Value Boundary Problems of Nonlinear PDE's

Abstract

We have designed a cubic spline wavelet decomposition for the Sobolev space HO(2)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's. Wavelet

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1993
Accession Number
ADA272244

Entities

People

  • Jianzhong Wang
  • Wei Cai

Tags

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  • C4I

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Equations
  • Errors
  • Fluid Dynamics
  • Frequency
  • Frequency Domain
  • Mathematics
  • Notation
  • Numbers
  • Partial Differential Equations
  • Periodic Functions
  • Real Numbers

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  • Mathematics

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  • Approximation Theory.
  • Software Engineering.

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  • Space