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Zbl 1235.65086
Khuri, S.A.; Sayfy, A.
Troesch's problem: a B-spline collocation approach. (English)
[J] Math. Comput. Modelling 54, No. 9-10, 1907-1918 (2011). ISSN 0895-7177

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 2000:: *65L60 Finite numerical methods for ODE

Keywords: boundary values problems; Shishkin-type mesh; collocation; B-splines; Troesch's problem

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Zentralblatt MATH Berlin [Germany]