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Numerical solution of singularly perturbed two-point boundary value problems by spline in tension. (English) Zbl 1030.65087

Singularly perturbed boundary value problems for second-order ordinary differential equations are analyzed. In many situations equations of that type give rise to solutions possessing interior layers. The author uses spline approximation techniques to discretize the problem. With the help of a discrete maximum principle a convergence result uniformly in the singular perturbation parameter is proved.
Moreover, a detailed discussion of the error term confirms that tension spline methods lead to accurate numerical solutions in the case when the step-size is large in respect to the singular perturbation parameter. Finally, numerical test examples are presented.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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References:

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