Five-point boundary value problems for $n$-th order differential equations by solution matching

Abstract

For the ordinary differential equation

$$y^{\left(n\right)}=f\left(x,y,y^{\prime },y^{\prime \prime },\dots ,y^{\left(n-1\right)}\right),n\ge 3,$$

solutions of three-point boundary value problems on $\left[a,b\right]$ are matched with solutions of three-point boundary value problems on $\left[b,c\right]$ to obtain solutions satisfying five-point boundary conditions on $\left[a,c\right]$.