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Sinc and the numerical solution of fifth-order boundary value problems. (English) Zbl 1121.65087
The present paper deals with numerical methods for fifth-order two-point boundary value problems on the unit interval. Problems of that type arise from modelling viscoelastic flows. The author introduces the new class of sinc-Galerkin methods, a special variant of spectral Galerkin schemes, to solve the boundary value problem. The suggested methods admit an elegant treatment of the boundary conditions. As usual, the corresponding integral relations are approximated by quadrature sums. Finally, some numerical computations display the power of the suggested method in comparison to standard schemes.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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