Siddiqi, Shahid S.; Akram, Ghazala; Malik, Salman A. Nonpolynomial sextic spline method for the solution along with convergence of linear special case fifth-order two-point boundary value problems. (English) Zbl 1125.65072 Appl. Math. Comput. 190, No. 1, 532-541 (2007). The authors investigate the nonpolynomial sextic spline method for the solution along with convergence of linear special case fifth-order two-point boundary value problems. Using the continuity of the derivatives at the knots, the consistency relations in terms of values of the spline and its fifth derivatives at the knots along with consistent end conditions are determined. The nonpolynomial sextic spline solution approximating the analytic solution of the boundary value problem is discussed. An error bound of the solution is given. Examples are given to illustrate the methods discussed. Reviewer: Seenith Sivasundaram (Daytona Beach) Cited in 1 ReviewCited in 7 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations Keywords:nonpolynomial sextic spline; convergence; difference equations; end conditions; numerical examples; fifth-order two-point boundary value problems PDFBibTeX XMLCite \textit{S. S. Siddiqi} et al., Appl. Math. Comput. 190, No. 1, 532--541 (2007; Zbl 1125.65072) Full Text: DOI References: [1] Davies, A. R.; Karageorghis, A.; Phillips, T. N., Spectral Galerkin methods for the primary two-point boundary value problem in modelling viscoelastic flows, Int. J. Numer. Methods Engng., 26, 647-662 (1988) · Zbl 0635.73091 [2] Karageorghis, A.; Phillips, T. N.; Davies, A. R., Spectral collocation methods for primary two-point boundary value problem in modelling viscoelastic flows, Int. J. Numer. Methods Engng., 26, 805-813 (1988) · Zbl 0637.76008 [3] Agarwal, R. P., Boundary Value Problems For High Order Differential Equations (1986), World Scientific: World Scientific Singapore · Zbl 0598.65062 [4] Shahid S. Siddiqi, Ghazala Akram, Quintic spline solutions of fourth order boundary-value problems, Int. J. Numer. Anal. Modell., in press.; Shahid S. Siddiqi, Ghazala Akram, Quintic spline solutions of fourth order boundary-value problems, Int. J. Numer. Anal. Modell., in press. · Zbl 1132.65069 [5] Caglar, H. N.; Caglar, S. H.; Twizell, E. H., 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 [6] Siddiqi, Shahid S.; Akram, Ghazala, Sextic spline solution of fifth order boundary value problems, Appl. Math. Lett., 20, 591-597 (2007) · Zbl 1125.65071 [7] Siddiqi, Shahid. S.; Akram, Ghazala, Solution of fifth order boundary value problems using nonpolynomial spline technique, Appl. Math. Comput., 175, 1574-1581 (2006) · Zbl 1094.65072 [8] Khan, Muhammad Azam; Siraj-ul-Islam; Tirmizi, Ikram A.; Twizell, E. H.; Ashraf, Saadat, A class of methods based on non-polynomial sextic spline functions for the solution of a special fifth-order boundary-value problem, J. Math. Anal. Appl., 321, 651-660 (2006) · Zbl 1096.65070 [9] Usmani, Riaz A., Discrete methods for a boundary value problem with engineering applications, Math. Comput., 32, 144, 1087-1096 (1978) · Zbl 0387.65050 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.