Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method.  give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments.
['Stefano Maset']
I am writing a research paper on a idea The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. I am writing a research paper on a idea Part I: Convergence Results
[{"from": "human", "value": "I am writing a research paper on a idea The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. I am writing a research paper on a idea Part I: Convergence Results"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method.  give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments."}]