Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs

• Autorzy: Hani Akbari
• Języki publikacji: EN

Abstrakty

EN

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2−nN ) in the H 1 norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We present a structured approach for fast and effective evaluation of these integrals via trivariate connection coefficients. Due to the fast convergence rate, very good approximations are found at low levels and with low Coiflet degrees, hence the size of corresponding linear systems is small. Numerical experiments confirm these claims.

Słowa kluczowe

EN

general stationary elliptic BVPs; Robin boundary condition; orthogonal Coifman wavelets; trivariate connection coefficients; fast convergence

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: 23
• Numer: 1
• Strony: 17-27

Daty

wydano

2013

otrzymano

2012-02-24

poprawiono

2012-06-11

Twórcy

autor

Hani Akbari

• Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Bibliografia

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Identyfikatory

DOI

10.2478/amcs-2013-0002