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A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations. (English) Zbl 1070.65065

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.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
62L12 Sequential estimation
34B05 Linear boundary value problems for ordinary differential equations
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