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Fitted mesh $B$-spline collocation method for solving self-adjoint singularly perturbed boundary value problems. (English) Zbl 1073.65062
The article is concerned with singularly perturbed second-order boundary value problems in formally self-adjoint form. After transformation into normal form, the problem is treated numerically by collocation with $B$-splines. The mesh of collocation points is chosen piecewise uniform, with higher density in the layer regions. The main theorem states quadratic convergence of the method, which is illustrated also in several numerical examples.

65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L12Finite difference methods for ODE (numerical methods)
34B05Linear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)
Full Text: DOI
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