New a posteriori error estimates for singular boundary value problems (Q2574861)

This paper deals with the numerical solution of boundary value problems for ordinary differential equations \[ z'(t)= t^{-\alpha} f(t, z(t)),\;t\in (0,1],\;g(z(0), z(1))= 0,\;z(t)\in C[0,1], \] where the parameter \(\alpha\) determines the type of singularity. The convergence properties and performance of three different a posteriori error estimates for the numerical approximations computed by polynomial collocation methods are presented. The efficiency of a collocation code using either of available a posteriori estimates for global error is compared. Three numerical examples with an essential singularity \((\alpha> 1)\) are solved.