Well-conditioning for variable coefficient second order boundary value difference systems (Q1921254)

This paper deals with boundary value difference systems of the form \[ U(n+2)+A_1(n+1)U(n+1)+A_0(n+1)U(n)=f(n+1),\quad 0\leq n\leq N-2; \] \(U(0)=\varphi\), \(U(N)=\psi\), where \(A_i\in C^{r\times r}\), \(f,\varphi,\psi\in C^r\). Sufficient conditions for well-conditioning are expressed in terms of the data for the given problem. First the homogeneous and nonhomogeneous constant coefficient problems are considered. Finally the variable coefficient problem is treated.