Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is concerned with the long-time behaviour of the numerical solutions generated by Runge-Kutta (RK) methods for nonlinear neutral delay differential equations (NDDEs). It is proved that the numerical solutions produced by ( k , l )-algebraically stable RK methods are uniformly ultimately bounded. Some examples reveal that some RK methods completely preserve the long-time behaviour of the exact solutions to NDDEs for sufficiently small time stepsize h . As a comparison with the previous results, a numerical example which further illustrates our theoretical results is provided.
['Wansheng Wang']
I am writing a research paper on a idea Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations
[{"from": "human", "value": "I am writing a research paper on a idea Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is concerned with the long-time behaviour of the numerical solutions generated by Runge-Kutta (RK) methods for nonlinear neutral delay differential equations (NDDEs). It is proved that the numerical solutions produced by ( k , l )-algebraically stable RK methods are uniformly ultimately bounded. Some examples reveal that some RK methods completely preserve the long-time behaviour of the exact solutions to NDDEs for sufficiently small time stepsize h . As a comparison with the previous results, a numerical example which further illustrates our theoretical results is provided."}]