Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H1H1 semi-norm of the difference beten itself and the initial value problem solution.
['Stefan M. Filipov', 'Ivan D. Gospodinov', 'István Faragó']
I am writing a research paper on a idea Shooting-Projection Method for Two-Point Boundary Value Problems
[{"from": "human", "value": "I am writing a research paper on a idea Shooting-Projection Method for Two-Point Boundary Value Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H1H1 semi-norm of the difference beten itself and the initial value problem solution."}]