Monotone iterative technique for initial-value problems of nonlinear singular discrete systems
The authors consider the initial-value problem (IVP) for nonsingular discrete systems of the following type \[ Ax(k+1)=f(x,x(k)),\quad x(0)=C_0, \tag{1} \] where \(k\in M\), \(A\) is a real singular \(n\times n\) matrix, \(x(k) \in\mathbb R^n\), \(C_0\in\mathbb R^n\) is a constant vector and \(f\in C[M\times\mathbb R^n,\mathbb R^n]\), \(M=\{0,1,2,\dots\}\). They are seeking for lower and upper solutions for the IVP for the singular discrete system (1) and obtain monotone sequences which converge to extremal solutions of (1). An existence theorem and extremal solutions based on a monotone iterative technique are proved and a numerical example is also provided.
scientific article; zbMATH DE number 5355639
scientific article