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Sinc-Galerkin method for solving linear sixth-order boundary-value problems. (English) Zbl 1054.65085

A Galerkin method to solve linear sixth-order boundary-value problems is proposed. As basis functions the so-called Sinc-functions are used. These functions are advantageous for problems with singularities.
The linear system to compute the unknown coefficients is developed using an appropriate inner product. Three academic examples (without any singularities) provide a comparison between approximated and exact solutions.
A discussion about existing methods for systems of ordinary differential equations (ODEs) for two-point boundary value problems (including a scalar sixth-order ODE) and their advantages or disadvantages is missing.

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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References:

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