Lv, Xueqin; Cui, Minggen An efficient computational method for linear fifth-order two-point boundary value problems. (English) Zbl 1191.65103 J. Comput. Appl. Math. 234, No. 5, 1551-1558 (2010). This paper deals with an algorithm to solve general fifth-order two point BVPs in the reproducing kernel space. The authors give the exact solution denoted by series of the linear fifth-order BVPs, truncating the series, the approximate solution is obtained. Two examples are presented to demonstrate the computational efficiency of the method. Reviewer: Pavol Chocholatý (Bratislava) Cited in 1 ReviewCited in 19 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations Keywords:fifth-order BVPs; ordinary differential equation; reproducing kernel space PDF BibTeX XML Cite \textit{X. Lv} and \textit{M. Cui}, J. Comput. Appl. Math. 234, No. 5, 1551--1558 (2010; Zbl 1191.65103) Full Text: DOI OpenURL References: [1] Davies, A.R.; Karageoghis, A.; Phillips, T.N., Spectral glarkien methods for the primary two-point boundary-value problems in modeling viscelastic flows, Internat. J. numer. methods engrg., 26, 647-662, (1988) · Zbl 0635.73091 [2] Fyfe, D.J., Linear dependence relations connecting equal interval nth degree splines and their derivatives, J. inst. math. appl., 7, 398-406, (1971) · Zbl 0219.65010 [3] Karageoghis, A.; Phillips, T.N.; Davies, A.R., Spectral collocation methods for the primary two-point boundary-value problems in modeling viscelastic flows, Internat. J. numer. methods engrg., 26, 805-813, (1998) · Zbl 0637.76008 [4] G.L. Liu, New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique, in: Proceeding of the Conference of the 7th Modern Mathematics and Mechanics, Shanghai, 1997. [5] Agarwal, R.P., Boundary value problems for high order differential equations, (1986), World Scientific Singapore · Zbl 0598.65062 [6] 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 [7] Wazwaz, A.M., The numerical solution of fifth-order boundary-value problems by Adomian decomposition, J. comput. appl. math., 136, 259-270, (2001) · Zbl 0986.65072 [8] Siraj-ul-Islam; Khan, M.A., A numerical method based on nonpolynomial sextic spline functions for the solution of special fifth-order boundary value problems, Appl. math. comput., 181, 356-361, (2006) · Zbl 1148.65312 [9] Siddiqi, Shahid S.; Akram, Ghazala, Sextic spline solutions of fifth order boundary value problems, Appl. math. lett., 20, 591-597, (2007) · Zbl 1125.65071 [10] 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, Appl. math. comput., 190, 532-541, (2007) · Zbl 1125.65072 [11] 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 [12] 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 problems, J. math. anal. appl., 321, 651-660, (2006) · Zbl 1096.65070 [13] Caglar, Hikmet; Caglar, Nazam, Solution of fifth order boundary value problems by using local polynomial regression, Appl. math. comput., 186, 952-956, (2007) · Zbl 1118.65347 [14] Rashidinia, J.; Jalilian, R.; Farajeyan, K., Spline approximate solution of fifth-order boundary-value problem, solution of fifth order boundary value problems by using local polynomial regression, Appl. math. comput., 192, 107-112, (2007) · Zbl 1193.65132 [15] El-Gamel, Mohamed, Sinc and the numerical solution of fifth-order boundary value problems, Appl. math. comput., 187, 22, 1417-1433, (2006) · Zbl 1121.65087 [16] Li, Chunli; Cui, Minggen, The exact solution for solving a class of nonlinear operator equation in the reproducing kernel space, Appl. math. comput., 143, 2-3, 393-399, (2003) · Zbl 1034.47030 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.