| Abstract: |
| We introduce a new fixed point shooting method that replaces the classical continuous shooting technique with a sequence of discrete initial value problems. Each discrete problem is easy to solve and collectively provides a high fidelity approximation to the trajectory of the corresponding continuous boundary value problem. Using these trajectories, we then construct a difference equation approximation to the original boundary value problem and establish rigorous error bounds for the method. This discrete framework offers both theoretical and computational advantages, as difference equations are often simpler to analyze and implement while retaining strong approximation properties. To demonstrate the effectiveness of the method, we apply it to a right focal boundary value problem and highlight its accuracy and efficiency. |
|