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Finite-difference methods for the solution of special eighth-order boundary-value problems. (English) Zbl 0820.65046
A special eighth-order boundary value problem \(w^{(8)} = f(x,w)\), \(w^{(2i)} (a) = A_{2i}\), \(w^{(2i)} (b) = B_{2i}\), \(i = 0,1,2,3\) is considered. This problem is solved by the finite difference method. Methods with second-, fourth-, sixth- and eighth-order of convergence are described. The problem is resolved by transforming the original problem into a system of four second-order problems, with the familiar three- point finite difference method. For a concrete problem the numerical results are compared.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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