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Journal of Computational Physics 182, 149190 (2002) doi:10.1006/jcph.2002.7160
 

Summary: Journal of Computational Physics 182, 149190 (2002)
doi:10.1006/jcph.2002.7160
Adaptive Solution of Partial Differential
Equations in Multiwavelet Bases
B. Alpert,,1
G. Beylkin,,2
D. Gines, and L. Vozovoi,3,4,5
National Institute of Standards and Technology, Boulder, Colorado 80305-3328; Department of Applied
Mathematics, University of Colorado, Boulder, Colorado 80309-0526; and School
of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
E-mail: alpert@boulder.nist.gov, beykin@boulder.colorado.edu, david.gines@agilent.com, and vozovoi@bfr.co.il
Received January 17, 2002; revised June 10, 2002
We construct multiresolution representations of derivative and exponential opera-
tors with linear boundary conditions in multiwavelet bases and use them to develop
a simple, adaptive scheme for the solution of nonlinear, time-dependent partial dif-
ferential equations. The emphasis on hierarchical representations of functions on
intervals helps to address issues of both high-order approximation and efficient ap-
plication of integral operators, and the lack of regularity of multiwavelets does not
preclude their use in representing differential operators. Comparisons with finite dif-
ference, finite element, and spectral element methods are presented, as are numerical

  

Source: Alpert, Bradley K. - Mathematical and Computational Sciences Division, National Institute of Standards and Technology (NIST)
Beylkin, Gregory - Department of Applied Mathematics, University of Colorado at Boulder

 

Collections: Computer Technologies and Information Sciences; Mathematics