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Solution of fifth order boundary value problems using nonpolynomial spline technique. (English) Zbl 1094.65072
Summary: Nonpolynomial spline is used for the numerical solutions of the fifth order linear special case boundary value problems. End conditions for the definition of spline are taken from [S. S. Siddiqi and Ghazala Akram, Sextic spline solutions of fifth order boundary value problems, Appl. Math. Lett.; to appear], consistent with the fifth order boundary value problem. H. N. Caglar, S. H. Caglar, and E. H. Twizell [Appl. Math. Lett. 12, No. 5, 25–30 (1999; Zbl 0941.65073)] presented the solution of a fifth order boundary value problem using a sixth degree B-spline which is first order convergent. The method presented in this paper is observed to be a second order convergent. For the numerical illustration of the method developed, an example is also considered.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
Citations:
Zbl 0941.65073
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[1] Karageorghis, A.; Phillips, T.N.; Davies, A.R., Spectral collocation methods for the primary two-point boundary-value problem in modelling viscoelastic flows, Int. J. numer. methods engng., 26, 805-813, (1988) · Zbl 0637.76008
[2] 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
[3] Caglar, H.N.; Caglar, S.H.; Twizell, E.H., The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions, Int. J. comput. math., 71, 373-381, (1999) · Zbl 0929.65048
[4] 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
[5] Usmani, Riaz A.; Sakai, Manabu, Quartic spline solutions for two-point boundary value problems involving third order differential equations, J. math. phys. sci., 18, 4, (1984) · Zbl 0583.65052
[6] Agarwal, R.P., Boundary value problems for high order differential equations, (1986), World Scientific Singapore · Zbl 0598.65062
[7] Siddiqi, S.S.; Twizell, E.H., Spline solution of linear sixth-order boundary value problems, Int. J. comput. math., 60, 3, 295-304, (1996) · Zbl 1001.65523
[8] Siddiqi, S.S.; Twizell, E.H., Spline solution of linear eighth-order boundary value problems, Comput. methods appl. mech. engng., 131, 309-325, (1996) · Zbl 0881.65076
[9] Siddiqi, S.S.; Twizell, E.H., Spline solution of linear tenth-order boundary value problems, Int. J. comput. math., 68, 3, 345-362, (1998) · Zbl 0920.65049
[10] Siddiqi, S.S.; Twizell, E.H., Spline solution of linear twelfth-order boundary value problems, J. comput. appl. math., 78, 371-390, (1997) · Zbl 0865.65059
[11] S.S. Siddiqi, Ghazala Akram, Sextic spline solutions of fifth order boundary value problems, Appl. Math. Lett., submitted for publication. · Zbl 1125.65071
[12] Siraj-ul-Islam; Muhammad Azam Khan; Tirmizi, Ikram A.; Twizell, E.H., Nonpolynomial spline approach to the solution of a system of third-order boundary value problems, Appl. math. comput., 168, 1, 152-163, (2005) · Zbl 1082.65553
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