Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with ak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. ll-posedness for the continuous problem as ll as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.
['David Amsallem', 'Jan Nordström']
I am writing a research paper on a idea High-order accurate difference schemes for the Hodgkin-Huxley equations
[{"from": "human", "value": "I am writing a research paper on a idea High-order accurate difference schemes for the Hodgkin-Huxley equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with ak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. ll-posedness for the continuous problem as ll as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees."}]