Coiflet–Galerkin method for solving second order BVPs with variable coefficients in three dimensions

Akbari, Hani; Kerayechian, Asghar

doi:10.1007/s11075-012-9558-x

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…A common choice of basis functions are finite element interpolation functions (Reddy, 2006;Ern and Guermond, 2004), but application of wavelets in the Galerkin method (for differential and integral equations) is too wide (Akbari and Kerayechian, 2012;Saberi et al, 2012;El-Gamel, 2006;Hashish et al, 2009;Nowak et al, 2010;Vampa et al, 2010).…”

Section: Consider Two Differential Operators L B In the Formsmentioning

confidence: 99%

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

Akbari¹

2013

International Journal of Applied Mathematics and Computer Science

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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.

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Section: Consider Two Differential Operators L B In the Formsmentioning

confidence: 99%

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

Akbari¹

2013

International Journal of Applied Mathematics and Computer Science

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“…However, several authors used other wavelet scaling functions for solving DE, e.g. symlets (sym), coiflets (coif), B-spline wavelets (bsp), biorthogonal (bior) and reversed biorthogonal (rbio) wavelets [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Solution of plane Dirichlet problem using compactly supported 2D wavelet scaling functions

Katunin

2012

Sci. Res. Inst. Math. Comp. Sci.

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Abstract. The paper presents the solution of the homogeneous plane Dirichlet problem using the wavelet-Galerkin method with various 2D compactly supported wavelet scaling functions. An analysis of approximation accuracy was performed with respect to the orders of investigated wavelet scaling functions and the level of approximation. The most effective scaling functions for solving the Dirichlet problem were indicated and discussed.

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Coiflet–Galerkin method for solving second order BVPs with variable coefficients in three dimensions

Cited by 2 publications

References 17 publications

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

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

Solution of plane Dirichlet problem using compactly supported 2D wavelet scaling functions

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