Shooting-Projection Method for Two-Point Boundary Value Problems
For researchers solving ODE boundary value problems, this offers a potentially simpler iterative approach, but the abstract lacks concrete performance metrics.
The paper introduces a shooting method for two-point boundary value problems that uses an iteration formula derived from an auxiliary function minimizing the H1 semi-norm. The method converges to the correct solution without numerical results reported.
This paper 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 H1 semi-norm of the difference between itself and the initial value problem solution.