Numerical solving of singular systems of ordinary differential equations of second order (Q1311144)

A boundary value problem for the system of differential equations \(A(t)x''+ B(t)x'+ C(t)x= f(t)\), \(A_ \alpha x(\alpha)+B_ \alpha x'(\alpha)= a\), \(A_ \beta x(\beta)+ B_ \beta x'(\beta)= b\) is studied where \(\text{det }A(t)= 0\). A finite difference method transforms it into a system of linear equations with a block-tridiagonal matrix which is solved by means of the matrix run-through method. Sufficient conditions are given under which this method is correct and stable.