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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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##### References:
 [1] Agarwal R. P., Boundary-Value Problems for Higher-Order Differential Equations (1986) · Zbl 0619.34019 [2] Ascher U. M., Numerical Solution of Boundary-Value Problems for Ordinary Differential Equations (1988) · Zbl 0671.65063 [3] DOI: 10.1080/00036818708839658 · Zbl 0588.76076 · doi:10.1080/00036818708839658 [4] DOI: 10.1098/rsta.1987.0051 · Zbl 0625.76043 · doi:10.1098/rsta.1987.0051 [5] DOI: 10.1016/0022-460X(89)91005-5 · Zbl 1235.74158 · doi:10.1016/0022-460X(89)91005-5 [6] Boutayeb A., Numerical Methods for Higher-Order Ordinary Differential Equations with Applications to Eigenvalue Problems (1990) [7] DOI: 10.1080/00207169208804130 · Zbl 0773.65055 · doi:10.1080/00207169208804130 [8] Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability (1961) [9] DOI: 10.1007/BF01931218 · Zbl 0401.65053 · doi:10.1007/BF01931218 [10] DOI: 10.1137/0716013 · Zbl 0438.65068 · doi:10.1137/0716013 [11] DOI: 10.1080/00036818008839296 · Zbl 0445.65078 · doi:10.1080/00036818008839296 [12] DOI: 10.1090/S0025-5718-1975-0371058-7 · doi:10.1090/S0025-5718-1975-0371058-7 [13] Khaliq A. Q. M., Numerical Methods for Ordinary Differential Equations with Applications to Partial Differential Equations (1983) [14] DOI: 10.1090/S0025-5718-1972-0373296-3 · doi:10.1090/S0025-5718-1972-0373296-3 [15] Lambert J. D., Numerical Methods for Ordinary Differential Systems (1991) · Zbl 0745.65049 [16] DOI: 10.1090/S0025-5718-1980-0559190-8 · doi:10.1090/S0025-5718-1980-0559190-8 [17] DOI: 10.1090/S0025-5718-1967-0223107-X · doi:10.1090/S0025-5718-1967-0223107-X [18] Tirmizi S. I. A., Numerical methods for Boundary-Value Problems with Applications to the Wave Equation (1984) [19] Twizell E. H., Numerical Mathematics Singapore 188 pp 495– (1988) [20] Twizell E. H., Proc. R. Soc. Lond. 431 pp 433– (1990) · Zbl 0722.65042 · doi:10.1098/rspa.1990.0142
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