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Galerkin-wavelet methods for two-point boundary value problems. (English) Zbl 0771.65050
Both the definition, basic properties and approximation properties of wavelets are described. The Galerkin method is applied to the numerical solution of the two-point boundary value problem $$-(q(x)u')'+r(x)u=f(x)$$ for $$x\in (0,R)$$ with Dirichlet (or mixed, or Neumann) condition, where the bases of a finite dimension solution subspace are formed by means of wavelet functions. Numerical examples are given.

MSC:
 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations
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References:
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