A numerical method based on polynomial sextic spline functions for the solution of special fifth-order boundary-value problems.

*(English)*Zbl 1148.65312Summary: A second-order accurate numerical scheme is presented for the solution of special fifth-order boundary-value problems with two-point-boundary conditions. The polynomial sextic spline functions are applied to construct the numerical algorithm. Convergence of the method is discussed through standard convergence analysis. A numerical illustration is given to show the pertinent features of the technique.

##### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

##### Keywords:

fifth-order boundary-value problem; polynomial sextic spline functions; numerical examples; two-point-boundary conditions; convergence
PDF
BibTeX
XML
Cite

\textit{Siraj-Ul-Islam} and \textit{M. Azam Khan}, Appl. Math. Comput. 181, No. 1, 356--361 (2006; Zbl 1148.65312)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Davies, A.R.; Karageoghis, A.; Phillips, T.N., Spectral Galerkin methods for the primary two-point boundary-value problem in modeling viscoelastic flows, Int. J. numer. methods eng., 26, 647-662, (1988) · Zbl 0635.73091 |

[2] | Karageoghis, A.; Phillips, T.N.; Davies, A.R., Spectral collocation methods for the primary two-point boundary-value problem in modeling viscoelastic flows, Int. J. numer. methods eng., 26, 805-813, (1988) · Zbl 0637.76008 |

[3] | Agarwal, R.P., Boundary-value problems for higher order differential equations, (1986), World Scientific Singapore · Zbl 0598.65062 |

[4] | M.S. Khan, Finite difference solutions of fifth-order boundary-value problems, PhD Thesis, Brunel University, England, 1994. |

[5] | Wazwaz, Abdul Majid, The numerical solution of fifth-order boundary-value problems by domain decomposition method, J. comput. appl. math., 136, 259-270, (2001) · Zbl 0986.65072 |

[6] | 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 |

[7] | Calgar, H.N., 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 |

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.