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Lamnii, A.; Mraoui, H.; Sbibih, D.; Tijini, A.; Zidna, A.

Sextic spline collocation methods for nonlinear fifth-order boundary value problems. (English) Zbl 1230.65086

Int. J. Comput. Math. 88, No. 10, 2072-2088 (2011).
The authors develop two sextic-spline collocation methods for approximating solutions of nonlinear fifth-order boundary-value problems. The first method uses a spline interpolant and the second one is based on a spline quasi-interpolant, which are constructed from sextic splines. Numerical examples confirm the second-order convergence predicted by the theoretical analysis.
Reviewer: Răzvan Răducanu (Iaşi)

Cited in 4 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations

Keywords:

fifth-order boundary value problems; collocation method; sextic spline interpolant; quasi-interpolant; numerical examples; convergence
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References:

[1] Agrawal R. P., Boundary Value Problems for High Order Differential Equations (1968)
[2] DOI: 10.1016/0022-247X(71)90110-7 · Zbl 0236.65020 · doi:10.1016/0022-247X(71)90110-7
[3] DOI: 10.1016/S0893-9659(99)00052-X · Zbl 0941.65073 · doi:10.1016/S0893-9659(99)00052-X
[4] DOI: 10.1002/nme.1620260309 · Zbl 0635.73091 · doi:10.1002/nme.1620260309
[5] DOI: 10.1016/j.amc.2006.09.049 · Zbl 1121.65087 · doi:10.1016/j.amc.2006.09.049
[6] DOI: 10.1016/j.camwa.2004.10.021 · Zbl 1072.65111 · doi:10.1016/j.camwa.2004.10.021
[7] DOI: 10.1002/nme.1620260404 · Zbl 0637.76008 · doi:10.1002/nme.1620260404
[8] Khan M. S., Finite-difference solution of fifth-order boundary-values problems (1994)
[9] DOI: 10.1016/j.jmaa.2005.08.023 · Zbl 1096.65070 · doi:10.1016/j.jmaa.2005.08.023
[10] Lamnii A., Math. Comput. Simulation 85 pp 1673– (2008)
[11] Schumeker, L. L. 1981. ”Spline Functions: Basic Theory”. New York: John Wiley and Sons.
[12] DOI: 10.1016/S0377-0427(00)00618-X · Zbl 0986.65072 · doi:10.1016/S0377-0427(00)00618-X
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