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Symmetrization of the sinc-Galerkin method for boundary value problems. (English) Zbl 0629.65085
The general Galerkin scheme applied to the boundary value problem $$ (1)\quad Lf(x)=f''(x)+\mu (x)f'(x)+\nu (x)f(x)=\sigma (x); $$ a$<x<b$, $f(a)=f(b)$, has the discrete form (2) $(Lf\sb m-\sigma,S\sb k)=0$, - M$\le k\le N$, where the $S\sb k$ are sinc functions composed with conformal maps. In the selfadjoint case of (1) the sinc-Galerkin coefficient matrix generated by (2) is nonsymmetric. The discrete Galerkin system is very much dependent on the choice of the weight function for (2). The author shows that by changing the weight function from what was used by {\it F. Stenger} [ibid. 33, 85-109 (1979; Zbl 0402.65053)], the symmetry of the discrete system is preserved. It is shown that for the appropriate selection of the mesh size, the error for the symmetrized sinc-Galerkin method and the error for the method by Stenger are asymptotically equal. The presented method still handles a wide class of singular problems.
Reviewer: P.ChocholatĂ˝

65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B05Linear boundary value problems for ODE
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