Global convergence method for singularly perturbed boundary value problems (Q557696)

A spline collocation method using the continuity condition of the first derivative of fitted exponential splines at the nodes is presented. The author uses splines fitted with a delta sequence as numerical strategies for the solution of the boundary value problem \(-\varepsilon u''+ p(x)u'+ q(x)u= f(x)\), \(u(a)= \alpha_0\), \(u(b)= \alpha_1\). The advantage of the convergence between the mesh points and the explicit form of the approximate solution is mentioned.