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**A smooth approximation based on exponential spline solutions for nonlinear fourth order two point boundary value problems.**
*(English)*
Zbl 1218.65075

Summary: Methods of order two, four and six based on exponential spline functions consisting of a polynomial part of degree three and an exponential part are developed to find approximations of linear and nonlinear fourth order two point boundary value problems. It is shown that the free parameter \(k\) of the exponential part can be used to raise the order of accuracy of the new scheme. A convergence analysis of these methods is given. Numerical examples for each the linear and the nonlinear case are included to illustrate the practical usefulness of our methods.

### MSC:

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

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

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

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

34B15 | Nonlinear boundary value problems for ordinary differential equations |

65L70 | Error bounds for numerical methods for ordinary differential equations |

### Keywords:

exponential spline; quintic spline; finite difference; two-point boundary value problem; error bound; convergence; numerical examples
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\textit{W. K. Zahra}, Appl. Math. Comput. 217, No. 21, 8447--8457 (2011; Zbl 1218.65075)

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### References:

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