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**Quadratic non-polynomial spline approach to the solution of a system of second-order boundary-value problems.**
*(English)*
Zbl 1100.65067

Summary: A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis of the method is discussed. A numerical example is given to illustrate practical usefulness of the new method.

### MSC:

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

34B05 | Linear boundary value problems for ordinary differential equations |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

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

74M15 | Contact in solid mechanics |

65L12 | Finite difference and finite volume methods for ordinary differential equations |

### Keywords:

non-polynomial splines; quadratic spline functions; finite-difference methods; obstacle problems; boundary-value problems; comparison of methods; contact problems; collocation; finite-difference; convergence; numerical example
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\textit{Siraj-Ul-Islam} et al., Appl. Math. Comput. 179, No. 1, 153--160 (2006; Zbl 1100.65067)

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### References:

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[11] | Siraj-ul-Islam; Azam Khan, M.; Tirmizi, I.A.; Twizell, E.H., Non-polynomial 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 |

[12] | Siraj-ul-Islam, I.A Tirmizi, Non-polynomial spline approach to the solution of a system of second-order boundary-value problems, Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.04.064. · Zbl 1088.65073 |

[13] | Siraj-ul-Islam, I.A Tirmizi, Saadat Ashraf, A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications, Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.06.006. · Zbl 1138.65303 |

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