Abstract
An error bound for the collocation method by spline in tension is developed for a nonlinear boundary value problemay″+by′+cy=f(·,y),y(0)=y 0,y(1)=y 1. Sharp error bounds for the interpolating splines in tension are used in conjunction with recently obtained formulae for B-splines, to develop an error bound depending on the tension parameters and net spacing. For singularly perturbed boundary value problems (|a|=ε≪1), the representation of the error motivates a choice of tension parameters which makes the convergence of the collocation method problem at least linear. The B-representation of the spline in tension is also used in the actual computations. Some numerical experiments are given to illustrate the theory.
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Communicated by L.L. Schumaker
Supported by grant 1-01-254 of the Ministry of Science and Technology, Croatia.
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Marušić, M., Rogina, M. A collocation method for singularly perturbed two-point boundary value problems with splines in tension. Adv Comput Math 6, 65–76 (1996). https://doi.org/10.1007/BF02127696
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DOI: https://doi.org/10.1007/BF02127696