Numerical solution of singularly perturbed two-point boundary value problems by spline in tension
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.
scientific article; zbMATH DE number 1861169
scientific article