Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate collocation methods for the efficient solution of singular boundary value problems with an essential singularity.  give numerical evidence that this approach indeed yields high order solutions. Moreover,  discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a singularity of the first kind, is less robust with respect to an essential singularity than a classical strategy based on mesh halving.
['Winfried Auzinger', 'Othmar Koch', 'Ewa Weinmüller']
I am writing a research paper on a idea Collocation methods for boundary value problems with an essential singularity
[{"from": "human", "value": "I am writing a research paper on a idea Collocation methods for boundary value problems with an essential singularity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate collocation methods for the efficient solution of singular boundary value problems with an essential singularity.  give numerical evidence that this approach indeed yields high order solutions. Moreover,  discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a singularity of the first kind, is less robust with respect to an essential singularity than a classical strategy based on mesh halving."}]