Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  discuss a leading-edge model used in the computation of the run-out length of dry-flowing avalanches. The model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics. Existence, uniqueness and smoothness properties of the analytical solution are shown.  also prove the existence of a unique root of the solution. Moreover,  present a FORTRAN 90 code for the numerical computation of the run-out length. The code is based on a solver for singular initial value problems which is an implementation of the acceleration technique known as iterated defect correction based on the implicit Euler method.
['Othmar Koch', 'Ewa Weinmüller']
I am writing a research paper on a idea Analytical and numerical treatment of a singular initial value problem in avalanche modeling
[{"from": "human", "value": "I am writing a research paper on a idea Analytical and numerical treatment of a singular initial value problem in avalanche modeling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  discuss a leading-edge model used in the computation of the run-out length of dry-flowing avalanches. The model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics. Existence, uniqueness and smoothness properties of the analytical solution are shown.  also prove the existence of a unique root of the solution. Moreover,  present a FORTRAN 90 code for the numerical computation of the run-out length. The code is based on a solver for singular initial value problems which is an implementation of the acceleration technique known as iterated defect correction based on the implicit Euler method."}]