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The algorithms of selected methods for the two-point boundary value problem for the equation - u" + g(x)u = f(x)

100%

Kołodziejczyk J., Grabarski A.

Mathematica Applicanda

1990

tom 18

nr 32

In this paper four algorithms of methods of approximate solution of the two-point boundary value problem for the equation - u” + g(x)u = f(x) are given and compared. The finite difference, collocation, finite element and collocation-Galerkin methods are considered. Numerical results are presented. For sufficiently regular functions u,f and g the finite difference method is the most effective.

Superconvergence effect in finite element methods for two-point boundary value problems

63%

Regińska T.

Mathematica Applicanda

1987

tom 16

nr 30

Approximate methods for solving two-point boundary value problems are considered. The aim of the paper is to explain superconvergence effect in the methods using finite element spaces. The existence of a class of the methods with the superconvergence property is demonstrated. Detailed proofs of superconvergence are presented for the case of the Galerkin method (due to Douglas and Dupont results) and for some example of external method.

H^(-1) Galerkin-collocation method with quadratures for two point boundary value problems

63%

Leyk Z.

Mathematica Applicanda

1989

tom 17

nr 31

In the paper, the H^(-1)Galerkin-collocation method with quadratures (instead of integrals) for two point boundary value problems is considered. Approximate solution is a piecewise polynomial of degree r. It is proved that the method is stable and the error in L2-norm is of order O(h^(r+1)) if the used quadrature is exact for polynomial of degree not greater than r+1.

Ograniczanie wyników

3 Mathematica Applicanda

1 Grabarski A.

1 Kołodziejczyk J.

1 Leyk Z.

1 Regińska T.

1 1990

1 1989

1 1987

Wyniki wyszukiwania

The algorithms of selected methods for the two-point boundary value problem for the equation - u" + g(x)u = f(x)

Superconvergence effect in finite element methods for two-point boundary value problems

H^(-1) Galerkin-collocation method with quadratures for two point boundary value problems