Deficient discrete cubic spline solution for a system of second order boundary value problems (Q403092)

This paper deals with a numerical approach to solve boundary value problems of the form \[ y''(x)= \begin{cases} f(x), &a\leq x\leq c,\\ g(x)y+f(x)+r, &c\leq x\leq d,\\ f(x), &d\leq x\leq b, \end{cases} \] subject to \(y(a)=\alpha\), \(y(b)=\beta\), where \(f,g\) are continuous functions on the interval \([c,d]\). A deficient discrete cubic spline is suggested to obtain approximate solutions. The authors show that their method is of second order for specific parameter values. An application to an obstacle boundary value problem illustrates their approach and compares it to the performance of several different methods from the literature.