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Scaling vectors and multiwavelets in numerical differential equations -- Some approximation-theoretic and numerical issues

Massopust, P.T.

Galerkin approximations and finite element methods for operator equations of the form Lu = f play an important role in the theory of numerical differential equations. This report summarizes some of the approximation-theoretic and numerical issues encountered in solving operator equations of the form Lu = f. Particular emphasis is placed on Galerkin and finite element approximations using multiwavelets. Examples are used to illustrate some of the issues.