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1 
Twopoint boundary value problems with piecewise constant coefficients: weak solution and exact discretizationWindisch, G. 30 October 1998 (has links) (PDF)
For twopoint boundary value problems in weak formulation with piecewise constant coefficients and piecewise continuous righthand side functions we derive a representation of its weak solution by local Green's functions. Then we use it to generate exact threepoint discretizations by Galerkin's method on essentially arbitrary grids. The coarsest possible grid is the set of points at which the piecewise constant coefficients and the right hand side functions are discontinuous. This grid can be refined to resolve any solution properties like boundary and interior layers much more correctly. The proper basis functions for the Galerkin method are entirely defined by the local Green's functions. The exact discretizations are of completely exponentially fitted type and stable. The system matrices of the resulting tridiagonal systems of linear equations are in any case irreducible Mmatrices with a uniformly bounded norm of its inverse.

2 
Twopoint boundary value problems with piecewise constant coefficients: weak solution and exact discretizationWindisch, G. 30 October 1998 (has links)
For twopoint boundary value problems in weak formulation with piecewise constant coefficients and piecewise continuous righthand side functions we derive a representation of its weak solution by local Green's functions. Then we use it to generate exact threepoint discretizations by Galerkin's method on essentially arbitrary grids. The coarsest possible grid is the set of points at which the piecewise constant coefficients and the right hand side functions are discontinuous. This grid can be refined to resolve any solution properties like boundary and interior layers much more correctly. The proper basis functions for the Galerkin method are entirely defined by the local Green's functions. The exact discretizations are of completely exponentially fitted type and stable. The system matrices of the resulting tridiagonal systems of linear equations are in any case irreducible Mmatrices with a uniformly bounded norm of its inverse.

3 
Exact discretizations of twopoint boundary value problemsWindisch, G. 30 October 1998 (has links) (PDF)
In the paper we construct exact threepoint discretizations of linear and nonlinear twopoint boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal Mmatrices in the linear case and Mfunctions in the nonlinear case.

4 
Exact discretizations of twopoint boundary value problemsWindisch, G. 30 October 1998 (has links)
In the paper we construct exact threepoint discretizations of linear and nonlinear twopoint boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal Mmatrices in the linear case and Mfunctions in the nonlinear case.

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