Approximate solutions of a boundary value problem for delay nonlinear difference equations with computer realization

A unique class of difference equations with non-instantaneous impulses is examined. These impulses begin abruptly at specified initial time points and continue over given finite discrete intervals. Additionally, the current state appears on the right side of the equation, preventing recursive solutions and necessitating approximate methods. This paper proposes an algorithm that constructs two monotone sequences of successive approximations toward the solution of the given problem. It is theoretically demonstrated that both sequences converge to the solution. This algorithm has been implemented through a C# program using a procedural programming approach and is applied to approximate specific examples, including a modified Ricker model with non-instantaneous impulses.