Numerical methods for the solution of special sixth-order boundary-value problems. (English) Zbl 0773.65055

A family of numerical methods is developed for the solution of special sixth-order boundary value problems \((d/dx)^6w=f(t,w)\), \(a<x<b\), where three boundary conditions are specified at each endpoint. Symmetric finite difference methods with second- to eighth-order convergence are contained in the family. Global extrapolation procedures on two and three grids, which increase the order of convergence, are outlined. Numerical experiments for a test problem suggest that global extrapolation makes its greatest gains when used with a large value of the step-size.


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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