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Summary: Solution of Time Dependent Diffusion Equations with
Variable Coefficients using Multiwavelets
appeared in J. Computational Physics, Vol. 150, pp. 394424, 1999.
A. Averbuch y , M. Israeli z and L. Vozovoi y
y School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
z Faculty of Computer Science, Technion, Haifa 32000, Israel
appeared in J. of Computational Physics,Vol. 150, pp. 394424, 1999
Abstract
A new numerical algorithm is developed for the solution of time dependent
differential equations of the diffusion type. It allows for an accurate and efficient
treatment of multidimensional problems with variable coefficients, nonlinearities
and general boundary conditions. For space discretization we use the multiwavelet
bases introduced in [1] which were then applied to the representation of differential
operators and functions of operators in [3]. An important advantage of multiwavelet
basis functions, is the fact that they are supported only on non overlapping subdo
mains . Thus multiwavelet bases are attractive for solving problems in finite (non
periodic) domains.
Boundary conditions are imposed with a penalty technique of [12], it can be
used to impose rather general boundary conditions.
The penalty approach was extended to a procedure for ensuring the continuity
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