Vol. 1, No. 1, 2008

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

Johnny Henderson, John Ehrke and Curtis Kunkel

Vol. 1 (2008), No. 1, 1–7
Abstract

For the ordinary differential equation

${y}^{\left(n\right)}=f\left(x,y,{y}^{\prime },{y}^{\prime \prime },\dots ,{y}^{\left(n-1\right)}\right),\phantom{\rule{2em}{0ex}}n\ge 3,$

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 $\left[a,c\right]$.

Keywords
boundary value problem, ordinary differential equation, solution matching
Primary: 34B15
Secondary: 34B10