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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
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.

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
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[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 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. · 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
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