zbMATH — the first resource for mathematics

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.

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
Full Text:
References:
 [1] Agarwal R. P., Boundary-Value Problems for Higher-Order Differential Equations (1986) · Zbl 0619.34019 [2] DOI: 10.1080/00036818708839658 · Zbl 0588.76076 · doi:10.1080/00036818708839658 [3] DOI: 10.1098/rsta.1987.0051 · Zbl 0625.76043 · doi:10.1098/rsta.1987.0051 [4] Boutayeb A., Numerical Methods for High-Order Ordinary Differential Equations with Applications to Eigenvalue Problems (1991) [5] Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability (1961) [6] DOI: 10.1007/BF01931218 · Zbl 0401.65053 · doi:10.1007/BF01931218 [7] DOI: 10.1080/03091928508219267 · doi:10.1080/03091928508219267 [8] DOI: 10.1086/154522 · doi:10.1086/154522 [9] Twizell E. H., Numerical Mathematics pp 495– (1988) [10] DOI: 10.1098/rspa.1990.0142 · Zbl 0722.65042 · doi:10.1098/rspa.1990.0142
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.