A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations (Q1767880)

This paper deals with a numerical method used to solve the singularly perturbed problem \(-\varepsilon y^{(4)} - a(x)y^{(3)} + b(x)y^{(2)}-c(x)y =-f(x)\), \(x\in (0,1)\), \(y(0)=p\), \(y(1)=q\), \(y''(0)= -r\), \(y''(1)= -s\). Using the boundary conditions the authors reduce this problem to a system of two second-order equations subject to Dirichlet boundary conditions. A classical finite-difference scheme to obtain numerical solutions for this system is presented. Four examples are given.