Shooting-Projection Method for Two-Point Boundary Value Problems

TL;DR

This paper introduces a new shooting-projection method for efficiently solving two-point boundary value problems in second order ODEs, utilizing an auxiliary function to improve convergence.

Contribution

The paper proposes a novel shooting-projection technique that employs an auxiliary function to enhance the accuracy and convergence of boundary value problem solutions.

Findings

Method achieves faster convergence than traditional shooting methods.

Auxiliary function minimizes the H1 semi-norm of the solution difference.

Applicable to a wide class of second order boundary value problems.

Abstract

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.