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Spline solutions of linear twelfth-order boundary-value problems. (English) Zbl 0865.65059
Twelfth-order boundary value problems are solved using twelfth-degree splines. These problems have the form \[ \begin{gathered} y^{(12)}(x) + \phi(x)y(x) = \psi(x), \quad -\infty < a \leq x \leq b < \infty \\ y^{(2k)}(a) =A_{2k},\quad y^{(2k)}(b) = B_{2k},\quad k=0,1,2,\dots,5, \end{gathered} \] where \(\phi(x), \psi(x)\) are continuous functions defined in the interval \([a,b]\) and \(A_{2k}, B_{2k}\) are real constants. Two numerical illustrations are given. It is observed that the developed algorithm is second-order convergent.
Reviewer: K.Najzar (Praha)

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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