The roles that shooting methods can play in the theory of discrete boundary value problems

Abstract

The purpose of this work is to move towards a more complete understanding of the roles that shooting methods can play in the theory of discrete boundary value problems. I take the position that shooting methods can have an important function in exploring discrete boundary value problems due to: their mutually compatible characteristics; their accessibility; and the significance and flexibility of their conclusions. My position is supported through the establishment of new theory and via exemplification.

Keywords:

• Boundary value problem
• shooting method
• existence of solutions
• first-order difference equation
• counting solutions
• non-existence of solutions

2010 Mathematics Subject Classification:

• 39A12

Disclosure statement

No potential conflict of interest was reported by the author(s).