The Class of various order numerical methods based on non-polynomial spline have been developed for the solution of linear and non-linear

sixth-order boundary value problems. We developed non-polynomial spline which contains a parameter $\rho$, act as the frequency of the trigonometric part of the spline function, when such parameter tends to zero the dened spline reduce into the septic polynomial spline, the consistency relation of non-polynomial spline derived in such a way that, to be fitted to approximate the solution of the given sixth-order boundary value problems. Boundary formulas are developed to associate with presented spline methods. Truncation errors are given, we developed the class of second, fourth, sixth and eight order methods. Convergence analysis has been proved. The obtained methods have been tested on nine examples, to illustrate practical usefulness of our approach. The results of our higher eight order method compare with the existing methods so far.

sixth-order boundary value problems. We developed non-polynomial spline which contains a parameter $\rho$, act as the frequency of the trigonometric part of the spline function, when such parameter tends to zero the dened spline reduce into the septic polynomial spline, the consistency relation of non-polynomial spline derived in such a way that, to be fitted to approximate the solution of the given sixth-order boundary value problems. Boundary formulas are developed to associate with presented spline methods. Truncation errors are given, we developed the class of second, fourth, sixth and eight order methods. Convergence analysis has been proved. The obtained methods have been tested on nine examples, to illustrate practical usefulness of our approach. The results of our higher eight order method compare with the existing methods so far.

Sixth-order boundary value problem, Non-polynomial spline, Bound- ary formulae, Convergence analysis

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Primary Language | en |
---|---|

Subjects | Mathematics |

Journal Section | Mathematics |

Authors |

Bibtex | ```
@research article { hujms446419,
journal = {Hacettepe Journal of Mathematics and Statistics},
issn = {2651-477X},
eissn = {2651-477X},
address = {Hacettepe University},
year = {2017},
volume = {46},
pages = {835 - 849},
doi = {},
title = {Convergence of the class of methods for solutions of certain sixth-order boundary value problems},
key = {cite},
author = {Farajeyan, K. and Rashidinia, J. and Jalilian, R.}
}
``` |

APA | Farajeyan, K , Rashidinia, J , Jalilian, R . (2017). Convergence of the class of methods for solutions of certain sixth-order boundary value problems. Hacettepe Journal of Mathematics and Statistics, 46 (5), 835-849. Retrieved from http://dergipark.gov.tr/hujms/issue/38493/446419 |

MLA | Farajeyan, K , Rashidinia, J , Jalilian, R . "Convergence of the class of methods for solutions of certain sixth-order boundary value problems". Hacettepe Journal of Mathematics and Statistics 46 (2017): 835-849 <http://dergipark.gov.tr/hujms/issue/38493/446419> |

Chicago | Farajeyan, K , Rashidinia, J , Jalilian, R . "Convergence of the class of methods for solutions of certain sixth-order boundary value problems". Hacettepe Journal of Mathematics and Statistics 46 (2017): 835-849 |

RIS | TY - JOUR T1 - Convergence of the class of methods for solutions of certain sixth-order boundary value problems AU - K. Farajeyan , J. Rashidinia , R. Jalilian Y1 - 2017 PY - 2017 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 835 EP - 849 VL - 46 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - |

EndNote | %0 Hacettepe Journal of Mathematics and Statistics Convergence of the class of methods for solutions of certain sixth-order boundary value problems %A K. Farajeyan , J. Rashidinia , R. Jalilian %T Convergence of the class of methods for solutions of certain sixth-order boundary value problems %D 2017 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 46 %N 5 %R %U |

ISNAD | Farajeyan, K. , Rashidinia, J. , Jalilian, R. . "Convergence of the class of methods for solutions of certain sixth-order boundary value problems". Hacettepe Journal of Mathematics and Statistics 46 / 5 (October 2017): 835-849. |