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Troesch’s problem: a B-spline collocation approach. (English) Zbl 1235.65086
Summary: A finite-element approach, based on cubic B-spline collocation, is presented for the numerical solution of Troesch’s problem. The method is used on both a uniform mesh and a piecewise-uniform Shishkin mesh, depending on the magnitude of the eigenvalues. This is due to the existence of a boundary layer at the right endpoint of the domain for relatively large eigenvalues. The problem is also solved using an adaptive spline collocation approach over a non-uniform mesh via exploiting an iterative scheme arising from Newton’s method.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
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