Siraj-Ul-Islam; Azam Khan, Muhammad A numerical method based on polynomial sextic spline functions for the solution of special fifth-order boundary-value problems. (English) Zbl 1148.65312 Appl. Math. Comput. 181, No. 1, 356-361 (2006). Summary: A second-order accurate numerical scheme is presented for the solution of special fifth-order boundary-value problems with two-point-boundary conditions. The polynomial sextic spline functions are applied to construct the numerical algorithm. Convergence of the method is discussed through standard convergence analysis. A numerical illustration is given to show the pertinent features of the technique. Cited in 10 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 65L20 Stability and convergence of numerical methods for ordinary differential equations Keywords:fifth-order boundary-value problem; polynomial sextic spline functions; numerical examples; two-point-boundary conditions; convergence PDF BibTeX XML Cite \textit{Siraj-Ul-Islam} and \textit{M. Azam Khan}, Appl. Math. Comput. 181, No. 1, 356--361 (2006; Zbl 1148.65312) Full Text: DOI References: [1] Davies, A. R.; Karageoghis, A.; Phillips, T. N., Spectral Galerkin methods for the primary two-point boundary-value problem in modeling viscoelastic flows, Int. J. Numer. Methods Eng., 26, 647-662 (1988) · Zbl 0635.73091 [2] Karageoghis, A.; Phillips, T. N.; Davies, A. R., Spectral collocation methods for the primary two-point boundary-value problem in modeling viscoelastic flows, Int. J. Numer. Methods Eng., 26, 805-813 (1988) · Zbl 0637.76008 [3] Agarwal, R. P., Boundary-Value Problems for Higher Order Differential Equations (1986), World Scientific: World Scientific Singapore · Zbl 0598.65062 [5] Wazwaz, Abdul Majid, The numerical solution of fifth-order boundary-value problems by domain decomposition method, J. Comput. Appl. Math., 136, 259-270 (2001) · Zbl 0986.65072 [6] Fyfe, D. J., Linear dependence relations connecting equal interval \(N\) th degree splines and their derivatives, J. Inst. Math. Appl., 7, 398-406 (1971) · Zbl 0219.65010 [7] Calgar, H. N., The numerical solution of fifth-order boundary-value problems with sixth-degree B-spline functions, Appl. Math. Lett., 12, 25-30 (1999) · Zbl 0941.65073 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.