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On some quadrature rules with Laplace end corrections

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Bożek B., Solak W., Szydełko Z.

Open Mathematics

2012

tom 10

nr 3

1172-1184

We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σi=1∞ f(i + 1/2) where f ∈ C 6 with its sixth derivative of constant sign on [m, ∞) and ∫ m∞ f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections, J. Comput. Appl. Math., 1991, 36(2), 251–253].

Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients

100%

Melnikov Y.

Open Mathematics

2010

tom 8

nr 1

53-72

Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable for equations with piecewise-constant coefficients.

Ograniczanie wyników

2 Open Mathematics

1 Bożek B.

1 Melnikov Y.

1 Solak W.

1 Szydełko Z.

1 2012

1 2010

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On some quadrature rules with Laplace end corrections

Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients