Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The efficient integration of systems of ODEs requires the use of adaptive step size able to adjust the computational effort while keeping some desired level of numerical accuracy. Traditional methods use synchronous solvers, where the most demanding equation imposes its time step to all others ODEs. More efficient methods can be developed if one can support asynchronous solvers enabling each ODE to be run with its own step size.   present the new (A)synchronous (E)rror-Based (C)ontrol step-size solver (AEC), that supports variable and independent step-size ODE integration. The new method is mainly asynchronous, being step size and synchronization controlled by error estimation information. A comparison beten AEC and quantized-based solvers is presented.
['Fernando J. Barros']
I am writing a research paper on a idea Asynchronous, polynomial ODE solvers based on error estimation
[{"from": "human", "value": "I am writing a research paper on a idea Asynchronous, polynomial ODE solvers based on error estimation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The efficient integration of systems of ODEs requires the use of adaptive step size able to adjust the computational effort while keeping some desired level of numerical accuracy. Traditional methods use synchronous solvers, where the most demanding equation imposes its time step to all others ODEs. More efficient methods can be developed if one can support asynchronous solvers enabling each ODE to be run with its own step size.   present the new (A)synchronous (E)rror-Based (C)ontrol step-size solver (AEC), that supports variable and independent step-size ODE integration. The new method is mainly asynchronous, being step size and synchronization controlled by error estimation information. A comparison beten AEC and quantized-based solvers is presented."}]