On the optimal convergence
Two three-point difference schemes are proposed for the numerical solution of a singularly perturbed boundary value problem \(-\varepsilon u''+p(x)u=f(x)\), \(u(0)=A\), \(u(1)=B\), \(0<\varepsilon\leq 1\), \(p,f\in C^ 2[0,1]\). The pointwise error estimation is \(O(\min(h^ 2,\varepsilon))\), the global one is \(O(h^ 2)\) where \(h\) is the step size of the discretization.
singularly perturbed boundary value problem
scientific article; zbMATH DE number 110388